Agreement about bit of society covered by official count (9)
I believe the answer is:
consensus
'agreement' is the definition.
(consensus is a kind of agreement)
'about bit of society covered by official count' is the wordplay.
'about' becomes 'on' (**).
'bit of' indicates taking the first letters.
'covered by' is an insertion indicator.
'official count' becomes 'census' (I've seen this before).
The first letter of 'society' is 's'.
'on'+'s'='ons'
'ons' going within 'census' is 'CONSENSUS'.
(Other definitions for consensus that I've seen before include "General opinion" , "Unanimity" , "General agreement" , "agreed" , "Majority view" .)