Darn green kit needing repair for school (12)
I believe the answer is:
kindergarten
'school' is the definition.
(I've seen this before)
'darn green kit needing repair' is the wordplay.
'needing repair' indicates an anagram (I've seen 'need of repair' mean this).
'darn'+'green'+'kit'='darngreenkit'
'darngreenkit' with letters rearranged gives 'KINDERGARTEN'.
'for' is the link.
(Other definitions for kindergarten that I've seen before include "Where master may be" , "Pre-school institution for little children" , "Infant school" , "Playgroup" , "minor institution" .)