Drunkard finally finished port (5)
I believe the answer is:
dover
'port' is the definition.
(I've seen this before)
'drunkard finally finished' is the wordplay.
'finally' suggests the final letters.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
The final letter of 'drunkard' is 'd'.
'd'+'over'='DOVER'
(Other definitions for dover that I've seen before include "Sort of sole" , "Cinque Port" , "The largest English ferry port" , "Roved around the English port" , "Be aware of" .)