One who's quick to obtain drink, holding head (7,2)
I believe the answer is:
snapper up
'one who's quick to obtain' is the definition.
(someone who snaps things up)
'drink holding head' is the wordplay.
I cannot quite see how this works, but
'head' could be 'napper' (informal term for someone's head) and 'napper' is found within the answer.
'drink' could be 'sup' (to sup is to drink) and 'sup' is located in the leftover letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
(Another definition for snapper up that I've seen is " Bargain hunter".)