Ideas came out in places of learning (9)
I believe the answer is:
academies
'places of learning' is the definition.
(I've seen this in another clue)
'ideas came out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'ideas'+'came'='ideascame'
'ideascame' anagrammed gives 'ACADEMIES'.
'in' acts as a link.
(Other definitions for academies that I've seen before include "specialised schools" , "Places of study" .)