Let me see rose cut in Italian region (6)
I believe the answer is:
umbria
'italian region' is the definition.
(Umbria is an example)
'let me see rose cut' is the wordplay.
'let me see' becomes 'um' (both might be said when hesitating).
'rose' becomes 'briar' (briar is a kind of rose).
'cut' means to remove the last letter.
'briar' with its last letter taken off is 'bria'.
'um'+'bria'='UMBRIA'
'in' is the link.
(Other definitions for umbria that I've seen before include "Mountainous region in central Italy" , "in the Tiber region" , "Italian region" , "part of Italy" , "hilly area of Italy" .)