Lover to get shot of in Derby (9)
I believe the answer is:
boyfriend
'lover' is the definition.
(boyfriend is a kind of lover)
'shot of in derby' is the wordplay.
'shot' indicates an anagram.
'of'+'in'+'derby'='ofinderby'
'ofinderby' is an anagram of 'BOYFRIEND'.
'to get' is the link.
(Other definitions for boyfriend that I've seen before include "subject of musical" , "Close associate" , "Young man" , "Close relationship with him" , "woman may hope to become union member" .)