Tyrant leaving to start game (5-3)
I believe the answer is:
bully-off
'start game' is the definition.
'bully off' can be an answer for 'start' (I have seen 'start of play' mean 'bully off' so perhaps 'start' could also mean 'bully off'). I am not certain of the 'game' bit.
'tyrant leaving' is the wordplay.
'tyrant' becomes 'bully' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'leaving' becomes 'off' (as in 'I'm off').
'bully'+'off'='BULLY-OFF'
'to' is the link.
Can you help me to learn more?
(Other definitions for bully-off that I've seen before include "Opening moment of a hockey match" , "Hockey's opening moment" , "(Re-)start hockey game" .)