Shadow chancellor John McDonnell said he and Labour leader Jeremy Corbyn would follow "tradition" by leaving their roles if the party lost an election.
Mr McDonnell said he "can't see" how he or Mr Corbyn could continue to lead if they failed to win power in such a vote.
In an interview with former Labour spin doctor Alastair Campbell, Mr McDonnell was quizzed on the subject of either himself or Mr Corbyn carrying on in their roles after an election defeat.
"I can't see... I think it is the same for my own personal position, I can't see so," he told Mr Campbell, in the interview with GQ.
"What we'd do is as the tradition, which is have an election for a new leader."
Mr McDonnell also said a woman should take over from the current leader, as he named shadow education secretary Angela Rayner as a possible successor to Mr Corbyn.
"I'm still of the view now that whoever comes after Jeremy has got to be a woman," he said.
"We've got to have a woman leader. If you look at the new youngsters that have come through, they are fantastic."
He added: "There is a whole range of women. Angela Rayner... There is a whole range of women and it's fantastic."
Despite discussing the process for successors to Mr Corbyn, the Labour number two said the Opposition party could "win a majority".
Prime Minister Boris Johnson has repeatedly asked for MPs to back a general election - though the request has been refused until he rules out a no-deal Brexit.
Mr McDonnell said Labour could win a fresh poll outright but should an election produce another hung parliament, his party would not strike any deals or form a coalition.
If working as a minority government fails, he said Labour would request an immediate return to the polls, invoking memories of 1974 when Britain held two elections, with the second giving Labour a slim majority.
The 68-year-old said it "doesn't matter" what comes first between either a general election and a second Brexit referendum - which Labour supports holding - and vouched that the party had overcome its problem with anti-Semitism.
Additional reporting by PA.
