Suggest having beer with member (6)
I believe the answer is:
allege
'suggest' is the definition.
'beer with member' is the wordplay.
'beer' becomes 'ale' (type of beer).
'with' means one lot of letters goes inside another.
'member' becomes 'leg' (member can mean a limb).
'ale' enclosing 'leg' is 'ALLEGE'.
'having' is the link.
(Other definitions for allege that I've seen before include "Declare or accuse without proof" , "Aver - maintain" , "Claim (a person is guilty)" , "Swear" , "Accuse without established proof" .)