The most common and most likely answer to this crossword clue is the 5 letter word DOVER
I've seen this crossword clue in The Guardian
D
O
V
E
R
More clues leading to the result DOVER
- Duke finished port
- Daughter having too much port
- Daughter finished the port
- Port extremely inadequate served at the end of party
- Port taking five hundred and six deliveries?
- Drunkard finally finished port
- Active person drinking very little port
- A number finished the port
- Start to despair having finished port
- Drive through English port
Buddy explains!

The straight part
We know that "the port" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the port = dover.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.