Staggers, giving drunken leers (5)
I believe the answer is:
reels
'staggers' is the definition.
('reel' can be a synonym of 'stagger')
'drunken leers' is the wordplay.
'drunken' indicates anagramming the letters.
'leers' is an anagram of 'REELS'.
'giving' is the link.
(Other definitions for reels that I've seen before include "Goes round and round" , "Scottish dances" , "Staggers about in Irish dances" , "performed by dancers" , "Cylinders on which cords are wound" .)