Serve drunk around midnight on the outskirts (6)
I believe the answer is:
verges
'the outskirts' is the definition.
(thesaurus)
'serve drunk around midnight' is the wordplay.
'drunk' indicates anagramming the letters.
'around' is an insertion indicator.
'midnight' becomes 'g' (**).
'serve' with letters rearranged gives 'veres'.
'veres' going around 'g' is 'VERGES'.
'on' is the link.
(Other definitions for verges that I've seen before include "Roadsides" , "Grass borders on roads" , "Edges or thresholds" , "Strips of grass bordering roads" , "Limits, boundaries or borders" .)