Head of department having finished port (5)
I believe the answer is:
dover
'port' is the definition.
(English port)
'head of department having finished' is the wordplay.
'head of' indicates taking the first letters.
'having' is a charade indicator (letters next to each other).
'finished' becomes 'over' (over can mean finished or ended).
The first letter of 'department' is 'd'.
'd'+'over'='DOVER'
(Other definitions for dover that I've seen before include "The largest English ferry port" , "Cinque Port" , "Kent ferry port" , "fish" , "Roved around the English port" .)