Wild overreaction describing student's debut in music school (13)
'music school' is the definition.
(I've seen this before)
'wild overreaction describing student's debut' is the wordplay.
'wild' indicates an anagram.
'describing' means one lot of letters goes inside another (describe can mean to form the outline of).
'debut' indicates taking the first letters.
The initial letter of 'students' is 's'.
'overreaction' anagrammed gives 'conervatoire'.
'conervatoire' going around 's' is 'CONSERVATOIRE'.
'in' acts as a link.
(Other definitions for conservatoire that I've seen before include "College of arts", "School of music", "Music college", "School of note".)