Old town hall snoop, one previously in corporation (9)

I believe the answer is:
prytaneum
This might be a double definition.
'old town hall snoop' is the first definition.
I can't judge whether this definition defines the answer.
'one previously in corporation' is the second definition.
The definition suggests a singular noun which matches the answer.
Can you help me to learn more?
(Another definition for prytaneum that I've seen is " ancient town hall".)
I've seen this clue in The Times and The Sunday Times.
Want a hint initially instead of a full solution?
Install my app