Relief mission, perhaps, bearing a bit of alcohol? (7)
I believe the answer is:
airdrop
'relief mission' is the definition.
(means of dropping supplies to people in need)
'bearing a bit of alcohol?' is the wordplay.
'bearing' becomes 'air' (both can mean an attitude or pose).
'a bit of alcohol?' becomes 'drop' (ie a drop of alcohol).
'air'+'drop'='AIRDROP'
'perhaps' is the link.
(Other definitions for airdrop that I've seen before include "Road rip (anag.)" , "Emergency delivery" , "Delivery of supplies by parachute" , "Parachuting of supplies" , "supplies sent down" .)