Private school on Crete redevelopment (6)
I believe the answer is:
secret
'private' is the definition.
('secret' can be similar in meaning to 'private')
'school on crete redevelopment' is the wordplay.
'school' becomes 's' (**).
'on' indicates putting letters inside.
'redevelopment' indicates anagramming the letters.
'crete' with letters rearranged gives 'ecret'.
's' placed inside 'ecret' is 'SECRET'.
(Other definitions for secret that I've seen before include "Private, or something private" , "Private, covert" , "Private; classified" , "It's not to be told" , "Not generally known" .)