Something you will grab finally with online search? (7)
I believe the answer is:
bequest
'something you will' is the definition.
(a bequest is willed in a will)
'grab finally with online search?' is the wordplay.
'finally' says to take the final letters.
'with' says to put letters next to each other.
'online' becomes 'e' (as in e-mail or e-commerce).
'search?' becomes 'quest' (quest is a kind of search).
The last letter of 'grab' is 'b'.
'b'+'e'+'quest'='BEQUEST'
(Other definitions for bequest that I've seen before include "Gift by will of personal property" , "Endowment, legacy" , "Gift left in will" , "Something gifted in a will" , "One left in will" .)