Constitutional?

 The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.

 

Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law. [emphasis added]

The above is the entire text of the clause in Article I of the U.S. Constitution that sets out the role of the Senate in an impeachment trial. I bold-faced that one phrase because it is important in the context of the current trial of Donald Trump. There is nothing in the text that even suggests, let alone days outright, that an officer cannot be impeached and tried after leaving office...and it is clear that if he or she has left office, the punishment of disqualification remains available in the event of conviction.

Why is it important that this be true? Let's take it out of the context of a president, and make it another impeachable officer--say, Secretary of the Treasury. Our hypothetical Secretary Badguy is charged with actually embezzling from the U.S. Treasury. The evidence is clear, and the House votes for impeachment. But before the trial can begin, Mr. Badguy sees the handwriting on the wall and resigns. Is there now to be no recourse for the Congress? "Sorry, he's out of office, no point in trying him now." That would leave him unpunished and still eligible to be appointed, or worse, elected to another position in the future.

So, yes, it must be Constitutional to try an officeholder whose term has expired or who had resigned.