Compelling points in favour of Conservative elected head of government (9)
I believe the answer is:
enforcing
'compelling' is the definition.
(enforcing is a kind of compelling)
'points in favour of conservative elected head of government' is the wordplay.
'points' becomes 'en' (compass points east and north).
'in favour of' becomes 'for' (being for a particular cause).
'conservative' becomes 'C' (UK political abbreviation).
'elected' becomes 'in' (in government).
'head of' says to take the initial letters.
The first letter of 'government' is 'g'.
'en'+'for'+'c'+'in'+'g'='ENFORCING'
(Another definition for enforcing that I've seen is " Ensuring observance of rules".)