That man travels round British Isles (8)
I believe the answer is:
hebrides
'isles' is the definition.
(I've seen this before)
'that man travels round british' is the wordplay.
'that man' becomes 'he'.
'travels' becomes 'rides' (riding is a kind of traveling**).
'round' means one lot of letters goes inside another.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'he'+'rides'='herides'
'herides' enclosing 'b' is 'HEBRIDES'.
(Other definitions for hebrides that I've seen before include "Strangely, his breed comes from Scottish archipelago" , "Does his breed come from west of Scotland?" , "Shipping Forecast area" , "Scottish islands" , "His breed comes from west of Scotland" .)