Yes, but I don't see that the left will adhere to the Constitution and Nancy made procedural changes to the House. I would now assume perhaps House impeachment procedures?
The HoR is within its Constitutional authority to impeach Trump while he remains in office. They would be stupid to do so, and one could certainly argue that his address to the demonstrators gathered in DC on 6 January in no way amounted to high crimes and misdemeanors; Alan Dershowitz has already made the case that Trump's speech was fully protected by the 1A. But the Constitution does not specify the meaning of "high crimes and misdemeanors", so a HoR can decide that on a political basis.
However the Senate will not have time to conduct a trial before Biden is inaugurated, so in any Constitutional sense a renewed impeachment would become a dead letter on 20 January. Since there is no time for a trial, votes to impeach in the HoR are simply political grievance by the Ds and virtue signaling by the Rs.
Should a D-controlled Senate attempt to conduct a trial after Biden is inaugurated, I suppose a legal case would have to be made to SCOTUS, perhaps on the Bill of Attainder basis I have already suggested. Unfortunately the SCOTUS record does not inspire confidence. Certainly Rs (*some* Rs) would make the political case to the American people that the trial would be a waste of time and resources, and only a cause for additional animosity and division among the public at large. I can't think of a better way to keep Trump's supporters fully motivated than by making him a political martyr; he would essentially become the King-maker for the next R nomination, and he would be in a power position for which there is no impeachment or even censure. The Ds are smart enough to know this so they will pursue with all vigor any "Trumped up" criminal charges they can conjure.