Age becomes Bill Paterson.

There's always been a calm sense of authority behind everything the Glasgow-born actor has done, ever since he arrived onstage in the 1970s in The Great Northern Welly Boot Show and The Cheviot, The Stag and the Black, Black Oil. These great popular works not only redefined contemporary theatre in Scotland, but introduced Paterson's dulcet tones to a world beyond the Citizens Theatre where his career had begun.

Forty years on, the 67-year-old is preparing for his first stage appearance in two years in And No More Shall We Part, Tom Holloway's moving play about an elderly couple coming to terms with their own mortality. Hampstead Theatre's production is being brought to the Traverse Theatre as part of its Edinburgh Festival Fringe season following an off-radar try-out run on home turf, where it proved to be a very quiet success story.

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"They're a very loving couple," Paterson says of his character, Don, and Pam, played by Dearbhla Molloy. "They have a very natural, normal relationship. Their kids are grown up, and they're two people who've loved each other all their lives. In the play you see them over the course of one evening, sitting, talking, until gradually you realise there's something else going on. It's a play that grips you."

Holloway, an Australian writer, took his play's title from a song by fellow countryman, Nick Cave. He wrote it after his mother died after suffering from cancer for six years. "He wished she'd had more choice in how she died," Paterson explains.

Mortality is something that's been on Paterson's mind a lot lately, ever since the recent loss of artistic polymath and adventurer, George Wyllie, aged 90. Paterson appeared onstage alongside Wyllie in the mid 1980s in Wyllie's all-too-prophetic vaudevillian critique of the world banking system, A Day Down A Goldmine. It was a show that mixed up a small-scale take on theatre of the absurd with some of Wyllie's self-styled scul?tures.

"George was unique," says Paterson. "It would be fantastic to do something about the corruption of banks now. It's a show that's much more of the zeitgeist than it was in the 1980s."

Paterson ended up doing it after the late Russell Hunter, who'd appeared in an early reading of the show, was unavailable. By that time, Paterson had moved out of doing regular theatre, and had appeared in films such as Comfort and Joy and The Killing Fields. "George said to me, 'I hear you're a bit of an actor. Maybe you could learn it better than that other fella.'"

It was a good-natured jibe designed to appeal to an actor's competitive spirit, but A Day Down A Goldmine went on to become an Edinburgh Festival Fringe hit. Parts of the play were filmed by Murray Grigor for The Why?sman, an impressionistic documentary on Wyllie.

"The last time I saw George was last year," Paterson remembers, "and we talked about doing A Day Down A Goldmine again. He was still a very tough man, but the show involved him lugging round these constructions of his, and there was no way he could lift that stuff then, so we talked about getting an attractive young man or a beautiful girl in the show."

Sadly, such plans never came to fruition. If they had, audiences might have seen Paterson onstage sooner. And No More Shall We Part, after all, not only marks Paterson's first stage appearance since Mike Bartlett's Earthquakes in London at the National Theatre's Cottesloe space in 2010, his first for a decade, it is also his first time on a Scottish stage for almost 20 years. That was in 1994 in Mikhail Bulgakov's A Mongrel's Heart at Edinburgh's Royal Lyceum Theatre. Prior to this Paterson had appeared in another Russian play, A Man With Connections, at the Traverse Theatre in 1988.

"I found it very good going back into the theatre again two years ago," Paterson says. "I really liked being in a company again, especially a company like the one for Earthquakes in London. Apart from Lia Williams, who's not that old, I hasten to add, the company was full of young people, which made me feel like this Ancient Mariner figure, and that really suited me."

With the establishment of the National Theatre of Scotland over the last half decade, it's perhaps surprising that Paterson hasn't been co-opted for some main-stage vehicle closer to his birthplace. In truth, there have been offers, but boring old logistics have got in the way.

"There were various reasons," Paterson says. "I was doing Law and Order, which scuppered one thing which the NTS were very generous offering me. But now we're doing this two-hander in Edinburgh, so I certainly wouldn't rule out me doing something in the future. At one point I think A Day Down A Goldmine would have been ideal for the NTS, but now Vicky Featherstone's leaving, let's see what happens."

Such an approach has worked well for Paterson, ever since his ambitions to be a teacher were curtailed when he was studying at what was then RSAMD and found himself trying out for the Citizens Theatre for Youth, a precursor to theatre in education company TAG. He toured schools for a year, and made his mainstage debut alongside Leonard Rossiter in a 1967 production of The Resistible Rise of Arturo Ui.

The 1970s brought the Welly Boot Show, which made Billy Connolly a star, and the show which Paterson says was "without doubt, the linchpin of my career", The Cheviot, The Stag and the Black, Black Oil. John McGrath's ceilidh play for 7:84 Scotland captured a crucial moment, politically and socially as much as artistically, and Paterson has spoken about it a lot over the last 30-odd years. All he'll say now is that "it was a coming together of everything we wanted to do – John Bett, Alex Norton and I – but had never got round to doing. All the other great things I've been involved in – The Singing Detective, The Crow Road and so on – they would have happened anyway, but The Cheviot was the one thing I was involved in that I think changed things."

David Hare's 1977 TV Play For Today, Licking Hitler, took Paterson away from the stage shortly after appearing in the original production of John Byrne's Writer's Cramp. Paterson nevertheless managed to navigate between appearing in the first production of Ariel Dorfman's Death and the Maiden and award-winning TV dramas such as Traffik.

Following And No More Shall We Part, he may well be making a speedy return to Scotland by way of a proposed stage production of a radio play he wrote for Stanley Baxter at Oran Mor as part of the venue's A Play, A Pie and A Pint phenomenon. With former 7:84 company member David MacLennan running that particular show, if it works out it will bring Paterson's career full circle in a way he clearly relishes.

"I'm not a lazy actor," he says, "but I'm not driven in a particularly competitive way either. Acting is a nice way to earn a living after a lot of people have retired. And if you're still acting in your sixties or seventies, you're not stealing roles from 23-year-olds."

And No More Shall We Part, Traverse Theatre, Edinburgh, www.traverse.co.uk