British sailor looking up port (4)
I believe the answer is:
baku
'port' is the definition.
(port in Azerbaijan)
'british sailor looking up' is the wordplay.
'british' becomes 'uk' (Great Britain).
'sailor' becomes 'ab' (abbreviation for able seaman).
'looking up' says the letters should be written backwards (in a down clue, letters go up).
'uk'+'ab'='ukab'
'ukab' back-to-front is 'BAKU'.
(Other definitions for baku that I've seen before include "Azerbaijan's capital" , "Caspian Sea port" , "Capital of Azerbaijan on shore of Caspian Sea" , "Capital city of Azerbaijan" .)