Remain US President without end (4)
I believe the answer is:
bide
'remain' is the definition.
(biding is a kind of remaining)
'us president without end' is the wordplay.
'us president' becomes 'Biden' (Joe Biden).
'without end' means to remove the last letter.
'biden' with its last letter taken off is 'BIDE'.
(Other definitions for bide that I've seen before include "Remain or stay (poetically)" , "Dwell, stay" , "To - one's time is to wait for the right opportunity" , "Remain (archaic)" , "Remain; await (time)" .)