Racecourse employee, one looking fixedly (about time) (7)
I believe the answer is:
starter
'racecourse employee' is the definition.
(someone starting a race)
'one looking fixedly about time' is the wordplay.
'one looking fixedly' becomes 'starer' (someone who stares).
'about' is an insertion indicator.
'time' becomes 't' (abbreviation).
'starer' enclosing 't' is 'STARTER'.
(Other definitions for starter that I've seen before include "Race gun firer" , "Type of home" , "One giving signal to begin race" , "First course for beginner" , "First course of meal" .)