As his time in Downing Street comes to an end, Keir Starmer has been joking with friends about what he might do after he stands down as prime minister.

He has teased that he might take a cookery course. “He needs it, he only makes two meals,” one friend said. Another not entirely serious suggestion was cutting his father-in-law’s hedge in the expectation that if he did well, he could graduate to lawns.

Another ally suggested he would climb some mountains – actual ones rather than the metaphorical ones than have impeded his political career over the last two years. Beyond that, his allies say, he has yet to decide.

“He’ll take his time to think about it,” one said. “He doesn’t know yet what his priority will be.” Veterans of Starmer’s Labour government – often accused of lacking direction or vision – may well wince in recognition.

But many of those who have worked closely with him agree that he is likely to end up doing something on the international stage, where he has garnered respect from fellow leaders, and is generally seen by voters as having been a success.

Starmer has faced frequent criticism about the amount of time he has spent overseas, with critics labelling him “never here Keir”. Only latterly has he argued that international and domestic affairs are “one and the same thing” because of the impact of one upon the other.

“He’s got an incredible amount of experience to offer,” one friend said. “It feels like he’ll end up doing something international-facing. That’s his comfort zone and also what he’s best at.” He is reportedly interested in the role of Nato secretary general, when there is a vacancy.

In the meantime, Starmer is heading to the backbenches, with Downing Street suggesting he will stay until the next election. Some of his friends are not so sure. “He hasn’t had the headspace to think about it yet. I don’t know where he’ll land,” one said.

But others believe he will be guided by his sense of duty: towards constituents, party and country. Local members in his central London seat have already urged him to stay on to prevent a byelection that could be won by the Greens.

Every former prime minister also needs to work out what role they will play for their successor. Allies say he will keep his counsel, with one adding that he would offer Andy Burnham advice in private if asked, rather than the more public route taken by Tony Blair.

“He was a pain in the ass and that says more about Tony than it ever did about Keir,” one ally said. Another added: “He’ll be more Gordon Brown than Tony Blair in every way. I can’t see him going off to make his millions. He’ll pick a cause he cares about and stick with it.”

How does Starmer regard his own legacy, beyond the long list of government achievements he has listed at every recent opportunity? In an interview with Sky News this week, he suggested he might be remembered as the person who “saved the Labour party” after the Jeremy Corbyn era.

“Everybody along the way said: ‘It’s not going to happen. You’re not going to do it. It’s not possible.’ And every time I said: ‘It is. You watched me do it. We did it and we won a general election.’ And, I’m very proud of that. So I shall walk out with pride,” Starmer said.

But while he has said he accepts his party moved against him, some of his friends worry the reality has not yet hit home. Starmer has spent the last few weeks in a flurry of prime ministerial activity: pushing major policy over the line at home, and on multiple trips abroad.

“I don’t know what it means for him when he wakes up next week and it’s quiet, and he doesn’t need to rush downstairs to meetings. And then when he turns on the radio, and somebody is talking about the prime minister, but it’s not him,” one said.

Another added: “He’s got to keep himself busy. His family are amazing: they will help.”

Some former prime ministers never seem to get over being out of office. Boris Johnson, for example, whose sign off at his final prime minister’s questions was “hasta la vista, baby”, is still said to believe he can make a comeback.

In contrast, the Starmer that friends see in private was there for his last parliamentary appearance on Wednesday, telling his family watching on: “To my wife and children: I love you.”

In the next few weeks, Starmer will spend time on holiday with his wife, Victoria, and two teenagers: almost every break during his time in office was interrupted by global events or affairs of state.

“I leave probably the most high-profile job in the country to the most important, which is to be the best dad I can to my kids and best husband I can to my wife,” he said last week.