PM remains, about to resign (7)
I believe the answer is:
asquith
'pm' is the definition.
(H. H. Asquith, UK prime minister 1908-1916)
'remains about to resign' is the wordplay.
'remains' becomes 'ash' (remains of a fire).
'about' means one lot of letters goes inside another.
'to resign' becomes 'quit' (to quit something is to resign from it).
'ash' placed around 'quit' is 'ASQUITH'.
(Other definitions for asquith that I've seen before include "Herbert - - , WW1 PM" , "Liberal prime minister, 1908 to 1916" , "PM in 1914" , "PM 1908-16" , "Former PM" .)