Fill a sudden gap when teacher's pet gets in both plays (4,4,3,6)

I believe the answer is:

step into the breach

I'm a little stuck... Click here to teach me more about this clue!

'fill a sudden gap when teacher's pet gets in both plays' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'teacher's pet gets in both plays' is the wordplay.
'gets' says to put letters next to each other.
'plays' is an anagram indicator.
'teachers'+'pet'+'in'+'both'='teacherspetinboth'
'teacherspetinboth' anagrammed gives 'STEP INTO THE BREACH'.

Can you help me to learn more?

(Another definition for step into the breach that I've seen is " Fill in".)

I've seen this clue in the Sydney Morning Herald.

Want a hint initially instead of a full solution? Install my app