Claim member's overcome by booze (6)
I believe the answer is:
allege
'claim' is the definition.
(to allege something is to make a claim)
'member's overcome by booze' is the wordplay.
'member' becomes 'leg' (member can mean a limb).
'overcome by' indicates putting letters inside.
'booze' becomes 'ale' (type of alcohol).
'leg' going within 'ale' is 'ALLEGE'.
(Other definitions for allege that I've seen before include "Aver - maintain" , "Declare without absolute proof" , "hold" , "Declare or assert without proof" , "Declare or accuse without proof" .)