Function popular when visiting the Home Counties (4)
I believe the answer is:
sine
'function' is the definition.
(mathematical function)
'popular when visiting the home counties' is the wordplay.
'popular' becomes 'in'.
'when visiting' indicates putting letters inside.
'the home counties' becomes 'se' (Home Counties in the South East of England).
'in' inserted within 'se' is 'SINE'.
(Other definitions for sine that I've seen before include "Mathematical function" , "Latin tag for indefinitely - . . . . die" , "Indispensable condition" , "Trigonometric function" , "Trigonometrical function" .)