Port has aged with time, extremely rarely (9)
I believe the answer is:
gateshead
'port' is the definition.
'has aged with time extremely rarely' is the wordplay.
'with' says to put letters next to each other.
'extremely' means to remove the middle letters.
'rarely' indicates anagramming the letters (rare can mean unusual or strange).
'time' with its middle removed is 'te'.
'has'+'aged'+'te'='hasagedte'
'hasagedte' is an anagram of 'GATESHEAD'.
(Other definitions for gateshead that I've seen before include "Town linked to Newcastle" , "Tyneside town" , "Northern town" , "place on Tyneside" .)