Endlessly travelled around, having left part of Wales (7)
I believe the answer is:
newport
'part of wales' is the definition.
(Welsh city)
'endlessly travelled around having left' is the wordplay.
'endlessly' means to remove the last letter.
'travelled' becomes 'went' (I've seen this before).
'around' says the letters should be written backwards.
'having left' becomes 'port' (I can't justify this - if you can you should give a lot more credence to this answer).
'went' with its last letter taken away is 'wen'.
'wen' backwards is 'new'.
'new'+'port'='NEWPORT'
(Other definitions for newport that I've seen before include "There's one in Mayo, Wales and New England" , "- - , IOW or RI" , "City of southeast Wales" , "Major IOW town" , "Welsh city on the Usk" .)