Quits about notices (7)
I believe the answer is:
resigns
'quits' is the definition.
(resigning is a kind of quiting)
'about notices' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'notices' becomes 'signs' ().
're'+'signs'='RESIGNS'
(Other definitions for resigns that I've seen before include "Gives up (a post)" , "does the honourable thing" , "Leaves job voluntarily" , "abdicates" .)