Port served by modern refuge (8)
I believe the answer is:
newhaven
'port' is the definition.
(I've seen this before)
'by modern refuge' is the wordplay.
'by' means one lot of letters go next to another.
'modern' becomes 'new' (associated in meaning).
'refuge' becomes 'haven' (I've seen this in another clue).
'new' put next to 'haven' is 'NEWHAVEN'.
'served' is the link.
(Other definitions for newhaven that I've seen before include "Location of Yale" , "Sussex port" , "English port" , "Ferry port" , "where Americans have a university" .)