The force said it was made aware of two people attempting to enter the base - where submarines that carry the UK's Trident nuclear deterrent are based - at around 5pm on Thursday.
A spokesperson said: "A 34-year-old man and 31-year-old woman have been arrested in connection and enquiries are ongoing."
According to the PA news agency, the man arrested is Iranian.
A Royal Navy spokesperson said: "Police Scotland have arrested two people who unsuccessfully attempted to enter HM Naval Base Clyde on Thursday 19 March.
"As the matter is subject to an ongoing investigation, we will not comment further."
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Sky's defence and security analyst Michael Clarke noted that the site in Faslane is "the biggest military base in Scotland", with around 6,000 to 7,000 people there, "both civilians and military".
"Faslane is probably Britain's most important single installation", he added. "We have seven attack submarines. And if they're all out of maintenance, then this is where they operate from."
The draft paper, by the Labour Growth Group and Good Growth Foundation, argues for a complete overhaul of Labour's economic strategy and messaging to prevent a far-right government.
Policy proposals are still being worked up, but include cutting income tax and abolishing national insurance. Options for how this could be funded include equalising capital gains tax with income tax in certain areas, reforming council tax or taxing landowners.
Sky News understands the report has been looked at by several cabinet ministers and potential leadership contenders.
Advisors to Health Secretary Wes Streeting, former deputy prime minister Angela Rayner and Greater Manchester Mayor Andy Burnham - all tipped as frontrunners to replace Sir Keir Starmer - are among those understood to have engaged with the work.
The report is expected to be published just after the May local elections - the crunch point at which the prime minister could face a leadership challenge if they go as badly as predicted.
Sir Keir has repeatedly insisted he will fight on, so anyone seeking to take him out would need the backing of 80 MPs.
There is a big question mark over who could get the numbers following the move to block Mr Burnham from standing in the Gorton and Denton by-election, which Labour lost.
However, the report being published at a vulnerable time piles fresh pressure on the prime minister, whose tanking poll ratings are often blamed on a failure to tackle the cost of living crisis and communicate who Labour is for.
This report will suggest policies to tackle the cost of living, as well as how Labour can sell them to the public.
It will say Labour needs to redesign the tax system to incentivise hard work, with greater incentives for entrepreneurs and small business owners.
And it will argue that voter anger is fuelled by the belief "doing the right thing" leaves them feeling shafted, and Labour must confront those who make money from taking advantage of people.
Mark McVitie, the Labour Growth Group's director, told Sky News: "Everyone in politics is correctly diagnosing the cost of living crisis. That's not enough. You go to the doctor because something's wrong, but you don't just want them to tell you you're ill and they care, you want them to find out why and fix it. That's what this project is aiming to do.
"Until we can do that and take on the vested interests profiting from the mess, we're just offering painkillers for a condition that keeps getting worse."
The Labour strategist said the party must be "laser focused on rewarding work and taking initiative".
He added: "When someone working 60 hour weeks as a nurse or running a small business is paying a higher marginal tax rate than an institutional landlord, that's not happening.
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"As a party we need to be squarely on the side of those putting in the work, taking risks and doing the right thing, and not afraid to confront the vested interests who will resist that change."
The paper has the draft title of Beveridge Report, named after a famous report by Sir William Beveridge, a key figure in designing Britain's welfare state.
Another focus will be on devolution, with the paper saying it should be vastly expanded so regional mayors have greater fiscal powers.
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More than 100 Labour MPs work with the Growth Group, whose parliamentary chair is former YouGov pollster Chris Curtis.
The group looks at ways to tear down barriers to economic growth, which the government says is one of its central missions.
The UK's economic forecaster the OBR has predicted GDP to grow by an average 1.5% a year from 2027 to 2030.
However many MPs fear voters will not feel any tangible benefit unless more is done to tackle the everyday cost of living.
Sir Keir began the year with a pledge to be "laser focused" on the cost of living, but the reset has been overshadowed by the Peter Mandelson scandal, while the war in Iran has threatened to push prices up further.
Dame Jenni hosted the BBC's Woman's Hour for more than 30 years, stepping down in 2020.
She received her damehood in recognition of her contribution to broadcasting in 2011.
She announced that she had been diagnosed with breast cancer in 2006.
Some of her interviewees on the Woman's Hour included former prime minister Margaret Thatcher, author Margaret Atwood and former secretary of state and presidential hopeful Hillary Clinton.
Tributes poured in for Dame Jenni, with outgoing BBC director-general Tim Davie saying: "This is incredibly sad news and our thoughts are with all of Dame Jenni's family and friends.
"Dame Jenni was, simply put, a broadcasting icon. Throughout her three groundbreaking decades on Woman's Hour, Jenni created a safe space for her audience thanks to her warmth, intelligence and courage.
"We shall all miss her terribly. Her legacy endures in the countless conversations she started, the many issues she championed and the lives she touched."
Mohit Bakaya, controller at BBC Radio 4 and director of BBC Speech Audio, said: "Jenni Murray was a formidable voice in British broadcasting who was warm, fearless and beloved by listeners.
"During her decades at Woman's Hour, she helped shape the national conversation with intelligence, rigour and a remarkable ability to connect with audiences.
"Jenni leaves an indelible legacy on generations of listeners. We are profoundly grateful for her outstanding contribution to Radio 4, and she will be deeply missed."
Dame Jenni leaves behind her husband, David Forgham, and her two children.
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The number of cases in the outbreak rose on Friday from 27 to 29, with 18 defined as confirmed and another 11 probable, according to the UK Health Security Agency (UKHSA). The cases include two students who have died.
Meningitis outbreak latest: Health officials reveal 'worst case scenario'
So far, all the meningitis cases have links to Kent after a so-called "superspreading event" at the Club Chemistry nightclub in Canterbury.
As health chiefs battle to contain the bacterial outbreak, Kent County Council's director of public health Dr Anjan Ghosh has speculated on three "rough" scenarios over the next four weeks.
At a briefing on Friday, he said one theory is that cases remain contained in Kent.
A second scenario, which he described as the "most likely", would involve people travelling off campus outside Kent and then spreading the bacteria to others within a household.
"They were incubating when they left, and then they become cases, and there are small household, sporadic clusters outside of Kent," said Dr Ghosh.
He stressed these cases would be "containable" and the risk of infection is low.
But a "worst-case scenario", which he said was "highly unlikely", could result in another cluster outside the county.
Ed Waller, deputy chief executive of NHS Kent and Medway, also said a request has been made for a further 5,000 doses of vaccine as part of a local programme to protect those most at risk.
Among the 18 confirmed cases, 13 have been identified by UKHSA as meningococcal group B. All cases have required hospital admission.
A 21-year-old student at the University of Kent and a sixth form pupil at Queen Elizabeth's Grammar School in Faversham have died in the current outbreak.
The UKHSA said four schools in Kent have confirmed cases of meningitis, while the London animation and games school Escape Studios said one of its students with links to the county had contracted meningitis.
Over 2,500 people have now been successfully vaccinated, and 9,840 doses of antibiotics have been administered at several sites in the county.
Large queues have formed at the sites, including at the University of Kent, although some were turned away on Friday. The same issue occurred on Thursday, which was explained as a staffing problem.
More meningitis vaccination centres are due to open across Kent to help meet demand.
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The UKHSA has now completed a genetic analysis of the meningitis bacteria.
Brendan Wren, professor of Microbial Pathogenesis at the London School of Hygiene and Tropical Medicine (LSHTM), said the strain circulating in Kent "appears to be a new subvariant" of a type of group B meningococci bacteria which "has been previously identified in the UK".
"The current Bexsero MenB vaccine is based on the cell surface antigens of MenB strains and should provide protection against the MenB ST-41/44 variant," he added.
Meanwhile, Paul Hunter, professor in medicine at the University of East Anglia, speculated that cases may have peaked.
"The incubation period, though a little uncertain, ranges from two to 10 days, so I think we can be fairly certain that the peak from the initial superspreading event will have already passed," he said.
Alison Mutch, senior coroner for South Manchester, recorded a verdict of hanging, saying he was the person who caused his own death.
But she did not come to the conclusion it was suicide, saying it was unclear whether the former world champion meant to take his own life.
The inquest, in Stockport, was told that Hatton was more than twice the alcohol drink drive limit at the time of his death, aged 46, in September last year.
Ms Mutch said police found no notes or anything that gave any suggestion of an intent to take his life.
He had been under the influence of alcohol and there were also brain changes identified by the pathologist at his post mortem as chronic traumatic encephalopathy (CTE) - a brain disease caused by repeated head trauma in contact sports like boxing.
The condition can cause mood swings, confusion and forgetfulness, things his family said they had noticed.
The coroner said it was not possible to determine how much of an impact this had had on his death, so she recorded a narrative verdict.
The inquest opened with some statements from several of Hatton's family members who painted a picture of a man who was deeply loved and appreciated by them - and for whom his death came as a shock.
His son Campbell said he was "fearless" inside the ring, but had struggled outside, having been open about his issues with mental health, drugs and alcohol.
But said before his death his father "was in the best place he'd been in years".
His former partner, Jennifer, the mother of his two daughters, echoed this. She called him an "active present and loving father - seeing the girls multiple times a week".
And she said when they went for dinner as a family on 12 September - the last time anyone saw him alive - he was making positive and detailed plans with the girls. He wanted the whole family to come and watch his upcoming fight in Dubai
The dinner was "fun" and he seemed "completely normal". After dropping his family off he told them he would see them in a couple of days.
DS Helen Grigalis from Greater Manchester Police then described the hours leading up to the boxer's death.
She said Ricky Hatton had not come out to meet his driver for an event as expected on 13 September.
His manager, Paul Speak, then arrived at his house around 6.30 in the morning the next day to pick him up for a flight to Dubai.
He tried calling him and opened the gate, and eventually used his own key.
He heard music coming from the games room - went in and found Mr Hatton already dead.
A post mortem had found evidence of alcohol being consumed in the hours before his death - when he died he was well over twice the drink drive limit - and of previous cocaine and cannabis use, but not as recently.
The inquest heard the pathologist had examined a brain sample and found changes unusual for someone his age - mostly commonly found in older adults with Alzheimers.
In 2023, the boxer spoke about his personal life and continuing mental health battles in a Sky documentary.
Hatton was the most popular British fighter of his era and tens of thousands of fans followed him to Las Vegas for his biggest fights.
"The Hitman" won the world title with a stunning win over favourite Kostya Tszyu in 2005 and went on to fight all-time greats such as Floyd Mayweather and Manny Pacquiao - ultimately losing.
In July, he announced he was coming out of retirement for a December bout in Dubai, 13 years on from his last pro fight. Hatton was meant to be flying there on the day he was found.
Thousands turned out on the streets of Greater Manchester for Hatton's funeral procession in October to pay their respects. The likes of Liam Gallagher, Andrew Flintoff, Wayne Rooney and Tyson Fury also attended.
His son, Campbell, 24, told the service: "I can't explain how much I'm going to miss you dad, and that we won't be making any new memories - but the ones we did I will cherish forever."
His daughters, Fearne, 12, and Millie, 13, also gave emotional tributes.
Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email jo@samaritans.org in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.