Couple having split, he, initially leaving her for a decisive struggle (3-7)

'her for a decisive struggle' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'couple having split he initially' is the wordplay.
'couple' becomes 'tie' (both can mean to join).
'having' says to put letters next to each other.
'split he initially' becomes 'breaker' (I can't justify this - if you can you should believe this answer much more).
'tie'+'breaker'='TIE-BREAKER'

'leaving' acts as a link.

Can you help me to learn more?