Power to clamp vehicles in church offices (10)

'church offices' is the definition.
The definition and answer can be both groups as well as being plural nouns.
Perhaps there's a link between them I don't understand?

'power to clamp vehicles' is the wordplay.
I cannot really understand how this works, but
'power' could be 'p' and 'p' is located in the answer.
'vehicles' could be 'cars' (car is a kind of vehicle) and 'cars' is found within the answer.
This may be the basis of the clue (or it may be nonsense).

'in' acts as a link.

Can you help me to learn more?