Number seen wandering round Home Counties in a state (9)
I believe the answer is:
tennessee
'a state' is the definition.
(Tennessee is an example)
'number seen wandering round home counties' is the wordplay.
'number' becomes 'ten' (ten is a kind of number).
'wandering' indicates an anagram.
'round' means one lot of letters goes inside another.
'home counties' becomes 'se'.
'seen' anagrammed gives 'nese'.
'nese' going around 'se' is 'nessee'.
'ten'+'nessee'='TENNESSEE'
'in' acts as a link.
(Other definitions for tennessee that I've seen before include "US state, capital Nashville" , "Teen sense observed in American state" , "American state, capital Nashville" , "playwright's assumed first name" , "Name of US dramatist" .)