Martial art expert's home in New Jersey area (5)
I believe the answer is:
ninja
'martial art expert's' is the definition.
(I've seen this before)
'home in new jersey area' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'in' is an insertion indicator.
'new jersey' becomes 'nj'.
'area' becomes 'a' (maths abbreviation).
'in' inserted into 'nj' is 'ninj'.
'ninj'+'a'='NINJA'
(Other definitions for ninja that I've seen before include "Eastern agent" , "agent from the east" , "Teenage Mutant ... Turtle (toy)" , "Deadly type" , "Medieval Japanese trained in martial arts, assassination and espionage" .)