Former prime minister doesn't start retreat (4)
I believe the answer is:
lair
'retreat' is the definition.
(both can mean a private hideout)
'former prime minister doesn't start' is the wordplay.
'former prime minister' becomes 'blair' (I've seen this before).
'doesn't start' means to remove the first letter.
'blair' with its first letter taken off is 'LAIR'.
(Other definitions for lair that I've seen before include "Habitation of a wild animal" , "Home to a wild animal" , "Study" , "Burrow" , "Animal's resting place" .)