Minister to cut, dressing back of hand (5)
I believe the answer is:
padre
'minister' is the definition.
(I've seen this before)
'cut dressing back of hand' is the wordplay.
'cut' becomes 'pare' (I've seen this before**).
'dressing' means one lot of letters goes inside another (a dressing is a kind of covering).
'back of' says to take the final letters.
The final letter of 'hand' is 'd'.
'pare' enclosing 'd' is 'PADRE'.
'to' is the link.
(Other definitions for padre that I've seen before include "Army chaplain" , "Cleric" , "Sky pilot (military slang)" , "Army serviceman?" , "Chaplain to armed forces" .)