Elderly head of state going to The Hill in old carriage demands concessions (5,2,6)

'elderly head' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'state going to the hill in old carriage demands concessions' is the wordplay.
I cannot really understand how this works, but
'state' could be 'hold' (hold is a kind of state) and 'hold' is found in the answer.
'to' is present in the answer.
'old' could be 'o' (common abbreviation eg in OE for Old English) and 'o' is present in the answer.
This explanation may well be incorrect...

'of' is the link.

Can you help me to learn more?