Acknowledge award of bequest (5)
I believe the answer is:
grant
This clue is a triple definition!
'acknowledge' is the first definition.
(I've seen this in another clue)
'award' is the second definition.
(synonyms)
'of' acts as a link.
'bequest' is the third definition.
(thesaurus)
(Other definitions for grant that I've seen before include "Award or concede" , "Give freely" , "Agree to - bursary" , "cash allowance?" , "Give or allow as a privilege" .)