Petition to refuse ousting leader about indulgence (8)
I believe the answer is:
entreaty
'petition' is the definition.
(both can mean a request)
'refuse ousting leader about indulgence' is the wordplay.
'refuse' becomes 'deny' (synonyms).
'ousting leader' means to remove the first letter (to oust is to remove).
'about' indicates putting letters inside.
'indulgence' becomes 'treat' (to indulge yourself is to treat yourself).
'deny' with its initial letter removed is 'eny'.
'eny' placed around 'treat' is 'ENTREATY'.
'to' acts as a link.
(Other definitions for entreaty that I've seen before include "Supplication" , "Appeal" , "Earnest plea" , "application for assistance" , "Earnest or urgent request" .)