Give up once Democrat's got in! (4)
I believe the answer is:
cede
'give up' is the definition.
(synonyms)
'once democrat's got in' is the wordplay.
'in' indicates a hidden word.
'CEDE' is hidden within 'once democrat got'.
(Other definitions for cede that I've seen before include "Surrender, give up" , "21 across" , "Allow" , "Give up (eg, power)" , "Give up rights or possession" .)