Slip! Republican's in East River! (3)
I believe the answer is:
err
'slip' is the definition.
(to err is to make an error)
'republican's in east river' is the wordplay.
'republican' becomes 'r' (abbreviation).
'in' means one lot of letters goes inside another.
'east' becomes 'e' (synonyms).
'river' becomes 'r' (abbreviation for river).
'e'+'r'='er'
'r' going into 'er' is 'ERR'.
(Other definitions for err that I've seen before include "have an affair?" , "Make mistakes" , "Boob" , "'To . . . is human, to forgive divine'" , "do something you shouldn't" .)