Happen to search for a legacy (7)
I believe the answer is:
bequest
'a legacy' is the definition.
(bequest is a kind of legacy)
'happen to search' is the wordplay.
'happen' becomes 'be'.
'to search' becomes 'quest' (I've seen this before).
'be'+'quest'='BEQUEST'
'for' is the link.
(Other definitions for bequest that I've seen before include "Gift by will of personal property" , "Gift left in will" , "One left in will" , "Something gifted in a will" , "Endowment, legacy" .)