Finally persuade Roman governor to remove hair (7)
I believe the answer is:
epilate
'remove hair' is the definition.
(I've seen this in another clue)
'finally persuade roman governor' is the wordplay.
'finally' says to take the final letters.
'roman governor' becomes 'pilate' (Pontius Pilate).
The final letter of 'persuade' is 'e'.
'e'+'pilate'='EPILATE'
'to' is the link.
(Other definitions for epilate that I've seen before include "Pull out hair" , "Shave" , "Remove hair by the roots" .)