Martin travelling round county (6)
I believe the answer is:
antrim
'county' is the definition.
(county of Northern Ireland)
'martin travelling' is the wordplay.
'travelling' indicates an anagram.
'martin' anagrammed gives 'ANTRIM'.
'round' acts as a link.
(Other definitions for antrim that I've seen before include "Irish county of musically green glens" , "NI town" , "County of Northern Ireland" , "Giant's Causeway county" , "18 down in Ulster" .)