Prime minister cutting head of state's hair (6)
I believe the answer is:
thatch
'hair' is the definition.
(thatch can mean a mass of hair)
'prime minister cutting head of state's' is the wordplay.
'prime minister' becomes 'thatcher'.
'cutting' indicates named letters should be taken away.
'head of state' becomes 'er' (abbreviation for Elizabeth Regina).
'thatcher' with 'er' taken away is 'THATCH'.
(Other definitions for thatch that I've seen before include "Old fashioned rural roof covering" , "part of House?" , "Rural roofing" , "nothing of interest to thief wanting roof lead" , "unusual roof" .)