Get carving in a cathedral in grave style (7)
I believe the answer is:
acutely
'in grave style' is the definition.
'get carving in a cathedral' is the wordplay.
'get carving' becomes 'cut' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' is an insertion indicator.
'cathedral' becomes 'ely' (ely is a cathedral city in cambridgeshire).
'a'+'ely'='aely'
'cut' put inside 'aely' is 'ACUTELY'.
(Other definitions for acutely that I've seen before include "Pointedly" , "In a shrewd way" , "Severely, keenly" , "Extremely" , "with severity" .)