Stay on, chief (6)
I believe the answer is:
remain
'stay' is the definition.
(I know that stay is a kind of remain)
'on chief' is the wordplay.
'on' becomes 're' (regarding).
'chief' becomes 'main' (synonyms).
're'+'main'='REMAIN'
(Other definitions for remain that I've seen before include "Stay behind" , "Old dance" , "Stay on after others have gone" , "Stay (in position)" , "Stay (in a place)" .)