Per the 20th amendment his term is up on 20 Jan 2021 with or without an election.
As far as I know there is no constitutional provision for he or Pence to remain in office beyond that date without being re-elected.
Who takes over? The leader of the Senate?
The State Legislatures will appoint their electors, whether there is voting or not.
There is no provision in the Constitution that even SUGGESTS individuals voting is the way to choose electors, never mind a provision that REQUIRES it.
The electors will vote on December 15, 2020, the Special Joint Session with Mike Pence in the chair will count the votes on January 5, 2021, and either Donald Trump or the new President will take the oath of office on January 20, 2021 at noon.
All this will take place whether there is a “Presidential election”, or there isn’t.