Delay interrupting student's instruction (8)
I believe the answer is:
tutelage
'instruction' is the definition.
(tutelage is a kind of instruction)
'delay interrupting student's' is the wordplay.
'delay' becomes 'lag' (lag is a kind of delay).
'interrupting' indicates putting letters inside.
'student' becomes 'tutee' (I've seen this before).
'lag' inserted into 'tutee' is 'TUTELAGE'.
(Other definitions for tutelage that I've seen before include "Protection" , "Schooling" , "Instruction by personal teacher" , "Office of tutor or guardian" , "Guardianship; instruction" .)