Agitate about rider’s first piece of tack (7)
I believe the answer is:
stirrup
'piece of tack' is the definition.
'agitate about rider's first' is the wordplay.
'agitate' becomes 'stirup' (stir up).
'about' is an insertion indicator.
'first' indicates taking the first letters.
The first letter of 'riders' is 'r'.
'stirup' enclosing 'r' is 'STIRRUP'.
(Other definitions for stirrup that I've seen before include "Equestrian foot support" , "Small thing needed in hearing" , "This helps one to hear" , "Rider's foot support" , "supporter?" .)