Function popular in the Home Counties (4)
I believe the answer is:
sine
'function' is the definition.
(mathematical function)
'popular in the home counties' is the wordplay.
'popular' becomes 'in'.
'in the' is an insertion indicator.
'home counties' becomes 'se'.
'in' going into 'se' is 'SINE'.
(Other definitions for sine that I've seen before include "Indispensable condition" , "Trig function" , "Trigonometrical function" , "Opposite/hypoteneuse" , "Mathematical function" .)