On a pier drunk out of doors (4-3)
I believe the answer is:
open air
'out of doors' is the definition.
(I've seen this before)
'on a pier drunk' is the wordplay.
'drunk' is an anagram indicator.
'on'+'a'+'pier'='onapier'
'onapier' with letters rearranged gives 'OPEN-AIR'.
(Other definitions for open air that I've seen before include "Out of doors" , "Out-of-doors" , "Outdoors - with no cover" , "natural setting" , "Outside" .)