Gave up getting plastered! (8)
I believe the answer is:
rendered
This clue is a double definition.
'gave up' is the first definition.
('render' can be a synonym of 'give up')
'plastered' is the second definition.
(I've seen this before)
'getting' is the link.
(Other definitions for rendered that I've seen before include "Melted down fat or gave performance" , "Made restitution" , "Given; plastered" , "Caused to become" , "Plastered; gave" .)