Visitors arrived in greater numbers around British seaside resort (9)
I believe the answer is:
morecambe
'resort' is the definition.
(I've seen this before)
'visitors arrived in greater numbers around british seaside' is the wordplay.
I cannot really understand how this works, but
'greater' could be 'more' and 'more' is found within the answer.
'around' could be 'ca' (circa) and 'ca' is found within the answer.
'british' could be 'b' (abbreviation e.g. in 'BBC') and 'b' is found in the answer.
The remaining letters 'me' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
(Other definitions for morecambe that I've seen before include "Eric -; - bay" , "seaside town" , "resort town" , "English resort" , "Lancashire seaside resort" .)