Pilgrim zips around inspiring Turkish port (5)
I believe the answer is:
izmir
'turkish port' is the definition.
(I've seen this before)
'pilgrim zips around inspiring' is the wordplay.
'inspiring' indicates the answer is hidden within the clue (the clue has breathed in or 'inspired' the answer).
'around' says the letters should be written in reverse.
'rimzi' is hidden within 'pilgrim zips'.
'rimzi' back-to-front is 'IZMIR'.
(Other definitions for izmir that I've seen before include "Turkish port, formerly Smyrna" , "Turkish city" , "Turkish seaport, formerly called Smyrna" , "Modern Smyrna" , "Seaport and naval base in western Turkey" .)