Not all presidents live (6)
I believe the answer is:
reside
'live' is the definition.
(residing is a kind of living)
'not all presidents' is the wordplay.
'not all' indicates the answer is hidden within the clue (only some of the letters).
'RESIDE' is hidden within 'presidents'.
(Other definitions for reside that I've seen before include "Occupy a place" , "Dwell permanently" , "Hang out with" , "Dwell in desire" , "Live in permanently" .)