Sprint to catch red coach? (7)
I believe the answer is:
teacher
'coach?' is the definition.
(coach is a kind of teacher)
'sprint to catch red' is the wordplay.
'sprint' becomes 'tear' (I've seen this in another clue).
'to catch' is an insertion indicator.
'red' becomes 'Che' (Che Guevara the Marxist revolutionary).
'tear' going around 'che' is 'TEACHER'.
(Other definitions for teacher that I've seen before include "One who might give lines" , "One who educates" , "one of the staff" , "Lecturer" , "Schoolmaster" .)