Become sick of beer, say (3)
I believe the answer is:
ail
'become sick' is the definition.
(I've seen this before)
'beer say' is the wordplay.
'beer' becomes 'ale' (I've seen this before).
'say' shows a homophone (sound like).
'ale' sounds like 'AIL'.
'of' acts as a link.
(Other definitions for ail that I've seen before include "Become unwell" , "Afflict -- feel unwell" , "Trouble, afflict; be sickly" , "upset" , "Afflict; suffer" .)