Acquired horse for gloomy music fan (4)
I believe the answer is:
goth
'gloomy music fan' is the definition.
(a fan of goth music)
'acquired horse' is the wordplay.
'acquired' becomes 'got' ('get' can be a synonym of 'acquire').
'horse' becomes 'h' (synonyms).
'got'+'h'='GOTH'
'for' acts as a link.
(Other definitions for goth that I've seen before include "Teutonic invader of the Roman Empire" , "One of an ancient Germanic nation" , "Old German; rock style" , "punk style" , "Old invader" .)