Well-known day school suffering setback (5)
I believe the answer is:
noted
'well-known' is the definition.
(I've seen this before)
'day school suffering setback' is the wordplay.
'day' becomes 'd' (abbreviation for day).
'school' becomes 'eton' (famous UK public school).
'suffering setback' says the letters should be written backwards.
'd'+'eton'='deton'
'deton' written backwards gives 'NOTED'.
(Other definitions for noted that I've seen before include "Famed" , "Made a record - celebrated" , "Like music" , "Remarkable" , "written down" .)