Sen. Paul has already told reporters in his state that he plans on running for re-election next year, and that he will not impose a term limit on himself. He says he wants to impose term limits on all members of Congress at the same time, but does not believe in limiting himself if a constitutional amendment is not adopted.
https://www.wbko.com/2021/02/25/sen-rand-paul-discusses-upcoming-plans-for-re-election-2022/ The only Class 3 Senators who have not yet announced whether they are running for re-election next year are Chuck Grassley, Patrick Leahy, and Ron Johnson.