General agreement excludes Tory count (6)

I believe the answer is:

census

I'm a little stuck... Click here to teach me more about this clue!

'count' is the definition.
(census is a kind of count)

I cannot understand how the rest of the clue works.

(Other definitions for census that I've seen before include "Periodic count by statisticians" , "Head-count" , "Periodic counting of the population" , "Official survey" , "Periodic count as of population" .)

I've seen this clue in The Sun.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.