Good on minister, shortly leaving the board (6)
I believe the answer is:
diving
'leaving the board' is the definition.
'good on minister shortly' is the wordplay.
'good' becomes 'g' (abbreviation).
'on' says to put letters next to each other.
'minister' becomes 'divine'.
'shortly' means to remove the last letter.
'divine' with its last letter taken off is 'divin'.
'g' after 'divin' is 'DIVING'.
(Other definitions for diving that I've seen before include "Throwing oneself into water" , "water event" , "Principles of right and wrong" , "Going under water" , "Plunging oneself into water" .)