Teaching union introducing delay in support for course (8)
I believe the answer is:
tutelage
'teaching' is the definition.
(I know that tutelage is a type of teaching)
'union introducing delay in support for course' is the wordplay.
'union' becomes 'tu' (abbreviation for trade union).
'introducing' indicates putting letters inside (some letters introduced or inserted into others).
'delay in' becomes 'lag' (lag is a kind of delay. I am not sure about the 'in' bit.).
'support for course' becomes 'tee' (support on a golf course).
'lag' placed into 'tee' is 'telage'.
'tu'+'telage'='TUTELAGE'
(Other definitions for tutelage that I've seen before include "Schooling" , "Instruction by personal teacher" , "Office of tutor or guardian" , "Guardianship; instruction" , "Protection" .)