Function popular when visiting the Kent area (4)
I believe the answer is:
sine
'function' is the definition.
(mathematical function)
'popular when visiting the kent area' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'when visiting' is an insertion indicator.
'the kent area' becomes 'se' (Kent is in the South East of England).
'in' going inside 'se' is 'SINE'.
(Other definitions for sine that I've seen before include "Opposite/hypoteneuse" , "Indefinitely, with no appointed date - . . . . die" , "Trigonometrical function" , "Mathematical function" , "Trig function" .)