Conservative HQ's prerogative? (5,2,6)

'conservative' is the definition.
(conservative can mean right-wing)

'hq's prerogative?' is the wordplay.
I cannot quite see how this works, but
'prerogative?' could be 'right' (prerogative is a kind of right) and 'right' is present in the answer.
'hq' could be 'centre' (centre can mean a headquarters or base) and 'centre' is located in the answer.
The remaining letters 'of' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...