Protective cover Queen got from prime minister (6)
I believe the answer is:
thatch
'protective cover' is the definition.
(as in a thatched roof)
'queen got from prime minister' is the wordplay.
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'got from' is a deletion indicator (some letters get out of the word).
'prime minister' becomes 'thatcher'.
'thatcher' with 'er' removed is 'THATCH'.
(Other definitions for thatch that I've seen before include "Rural roofing" , "Cover for house" , "Natural roof covering" , "part of House?" , "unusual roof" .)