...the impeachment process must be started while the person is in office. It has started (Trump was just impeached!), so that requirement is met. After that comes the Senate trial & 2 votes, the 1st to convict & remove from office (requires 2/3 of members present) & then the 2nd vote to bar from holding office in the future (requires a simple majority).
I don't believe there's any requirement that the person be a current office holder for the Senate trial & votes. In other words, the House could impeach while they're POTUS then they could leave office by resigning or their term expiring & the Senate trial & votes could still proceed. I'm no expert, & I may have missed something, but I don't believe the Constitution prohibits that.
I care most about the 2nd Senate vote, to bar from office, for obvious reasons. I've seen some legal folks argue that the Senate can't hold that vote if the person is no longer in office, but there's a major flaw in their argument:
Let's say the Senate votes to convict & remove the impeached president, & that vote is successful. It's my understanding, based on a consensus of legal folks I follow, that at the conclusion of that vote, the president is removed, gone, they no longer hold office. The Constitution is specific that the vote to bar from office comes AFTER the vote to convict & remove, so that means the Senate, by explicit instructions in the Constitution, is voting to bar someone WHO NO LONGER HOLDS OFFICE.
So, to argue that the Senate can't vote to bar someone who is no longer in office seems to be nonsense. (Yes I realize all of this might have to happen within the context of a Senate impeachment trial, but there is a degree of flexibility there for the Senate.)