Triumph for female going next in line (9)
I believe the answer is:
successor
'next in line' is the definition.
(thesaurus)
'triumph for female going' is the wordplay.
'triumph' becomes 'success' (I've seen this before).
'female' becomes 'f' (abbreviation).
'going' is a deletion indicator.
'for' with 'f' taken out is 'or'.
'success'+'or'='SUCCESSOR'
(Other definitions for successor that I've seen before include "One taking over from another" , "Follower (in post)" , "for one of the following people" , "Heir" , "One follows next in order" .)