Principal graduate at home (4)
I believe the answer is:
main
'principal' is the definition.
(both can mean major)
'graduate at home' is the wordplay.
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'ma'+'in'='MAIN'
(Other definitions for main that I've seen before include "Chief in importance" , "Most important - high seas?" , "Principal motivation" , "associated with the Spanish?" , "Dominant" .)