Appraisal idiots, people in the core of Ofsted (10)
I believe the answer is:
assessment
'appraisal' is the definition.
('assessment' can be a synonym of 'appraisal')
'idiots people in the core of ofsted' is the wordplay.
'idiots' becomes 'asses' (I've seen this before).
'people' becomes 'men' (man is a kind of person).
'in the' indicates putting letters inside.
'core of' says to take the centre.
The middle letters of 'ofsted' are 'st'.
'men' inserted within 'st' is 'sment'.
'asses'+'sment'='ASSESSMENT'
(Other definitions for assessment that I've seen before include "Judgement" , "amount to be paid" , "Appraisal" , "Survey" , "Process of valuation" .)