A rock cut in part of Birmingham (5)
I believe the answer is:
aston
'part of birmingham' is the definition.
(I've seen this before)
'a rock cut' is the wordplay.
'rock' becomes 'stone' (synonyms).
'cut' means to remove the last letter.
'stone' with its final letter taken away is 'ston'.
'a'+'ston'='ASTON'
'in' is the link.
(Other definitions for aston that I've seen before include "A Birmingham university" , "Area of Birmingham" , "- Villa, football club" , "and 20: Midlands football club" , "part of Birmingham" .)