Succeed with a will in their resolve (7)
I believe the answer is:
inherit
'succeed' is the definition.
(I've seen this before)
'will in their resolve' is the wordplay.
'will' says to put letters next to each other (I've seen this in other clues).
'resolve' is an anagram indicator (I've seen 'resolving' mean this).
'their' is an anagram of 'herit'.
'in' put next to 'herit' is 'INHERIT'.
'with a' acts as a link.
(Other definitions for inherit that I've seen before include "Receive as bequest from will" , "Receive as heir" , "Acquire from ancestors" , "Get what was left?" , "Be the recipient of" .)