Put back in rider's gear right after eventing debut (8)
I believe the answer is:
reinsert
'put back in' is the definition.
(insert for a second time)
'rider's gear right after eventing debut' is the wordplay.
'rider's gear' becomes 'reins' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'right' becomes 'rt' (abbreviation as in Rt Hon- the Right Honourable).
'after' means one lot of letters go next to another.
'debut' says to take the initial letters.
The first letter of 'eventing' is 'e'.
'rt' put after 'e' is 'ert'.
'reins'+'ert'='REINSERT'
Can you help me to learn more?
(Other definitions for reinsert that I've seen before include "Enter, sir! (anag) - put in again" , "plant back" , "Put back in" .)