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 can't justify this - if you can you should believe this answer much more).
'right' becomes 'rt' (abbreviation as in Rt Hon- the Right Honourable).
'after' means one lot of letters go next to another.
'debut' suggests taking the first 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" .)