Celebrated school raised doubts initially (5)
I believe the answer is:
noted
'celebrated' is the definition.
('noted' can be a synonym of 'celebrated')
'school raised doubts initially' is the wordplay.
'school' becomes 'eton' (famous UK public school**).
'raised' is a reversal indicator.
'initially' says to take the initial letters.
The first letter of 'doubts' is 'd'.
'eton' in reverse letter order is 'note'.
'note'+'d'='NOTED'
(Other definitions for noted that I've seen before include "saw" , "Observed - recorded" , "Like music" , "Widely known and esteemed" , "prominent" .)