Rex gets stuck into finest French port (5)
I believe the answer is:
brest
'french port' is the definition.
(a port city in brittany)
'rex gets stuck into finest' is the wordplay.
'rex' becomes 'r' (common abbreviation e.g. GR=George Rex, King Georg).
'gets stuck into' is an insertion indicator.
'finest' becomes 'best' ('best' can be similar in meaning to 'finest'**).
'r' placed inside 'best' is 'BREST'.
(Other definitions for brest that I've seen before include "Breton port" , "French Atlantic naval base" , "Port in Brittany" , "French warships here in Brittany" , "Naval base in Brittany" .)