Eastern governor shows pluck (7)
I believe the answer is:
epilate
'pluck' is the definition.
(to epilate is to pluck hairs out)
'eastern governor' is the wordplay.
'eastern' becomes 'e'.
'governor' becomes 'Pilate' (Pontius Pilate, Roman governor in Christ's time).
'e'+'pilate'='EPILATE'
'shows' acts as a link.
(Other definitions for epilate that I've seen before include "Remove hair by the roots" , "Pull out hair" , "Shave" .)