First-class place becomes seat of government (7,4)

'government' is the definition.
(I know that Capital city is a type of municipal corporation)

'first-class place becomes seat' is the wordplay.
I cannot quite see how this works, but
'first' could be 'capital' (I've seen this before) and 'capital' is found in the answer.
The remaining letters 'city' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'of' is the link.

Can you help me to learn more?