Check about university pass this month for the beautician (10)

'check about university' is the definition.
The definition suggests a singular noun which matches the answer.

'pass this month for the beautician' is the wordplay.
I cannot quite see how this works, but
'pass' could be 'rub' (rubbing is a kind of passing) and 'rub' is present in the answer.
'month' could be 'inst' (I've seen this before) and 'inst' is present in the answer.
The remaining letters 'ein' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?