Hesitate to oust leader in state (4)
I believe the answer is:
aver
'state' is the definition.
(both can mean to declare)
'hesitate to oust leader' is the wordplay.
'hesitate' becomes 'waver' (wavering is a kind of hesitating).
'to oust leader' means to remove the first letter.
'waver' with its first letter taken away is 'AVER'.
'in' is the link.
(Other definitions for aver that I've seen before include "Say firmly, rave if necessary" , "Swear" , "Formally assert" , "Declare positively" , "'Affirm, assert (4)'" .)