Local head of state losing power (8)
I believe the answer is:
resident
'local' is the definition.
(a resident of a particular area)
'head of state losing power' is the wordplay.
'head of state' becomes 'president' (president is a type of head of state).
'losing' is a deletion indicator.
'power' becomes 'p' (symbol in physics).
'president' with 'p' removed is 'RESIDENT'.
(Other definitions for resident that I've seen before include "Inserted by permanent inhabitant" , "one in the house?" , "Citizen" , "Permanent dweller" , "One living somewhere" .)