Drunkard ultimately finished port (5)
I believe the answer is:
dover
'port' is the definition.
(port town in Kent)
'drunkard ultimately finished' is the wordplay.
'ultimately' suggests the final letters.
'finished' becomes 'over' (over can mean finished or ended).
The last letter of 'drunkard' is 'd'.
'd'+'over'='DOVER'
(Other definitions for dover that I've seen before include "fish" , "Be aware of" , "Kentish port" , "There'll be blue clouds over the white cliffs here" , "The largest English ferry port" .)