To succeed, it must follow her in first (7)
I believe the answer is:
inherit
'to succeed' is the definition.
(I've seen this before)
'it must follow her in first' is the wordplay.
'must follow' means one lot of letters go next to another.
'first' is a charade indicator (letters next to each other).
'it' put after 'her' is 'herit'.
'herit' put after 'in' is 'INHERIT'.
(Other definitions for inherit that I've seen before include "Be bequeathed" , "Get what was left?" , "Receive as heir" , "Succeed as heir" , "Receive from a predecessor" .)