Make fine cut (5)
I believe the answer is:
fetch
'make' is the definition.
(thesaurus)
'fine cut' is the wordplay.
'fine' becomes 'f' (abbreviation).
'cut' becomes 'etch' (I've seen this before).
'f'+'etch'='FETCH'
(Other definitions for fetch that I've seen before include "Order to dog to retrieve thrown stick" , "Go and get back, like dog with stick" , "Go and bring back" , "Command to a gun dog" , "Collect" .)