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Reduced price at the barber's? (3,4)

Ross

I believe the answer is:

cut rate

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

'reduced price' is the definition.
(I've seen this before)

'at the barber's?' is the wordplay.
I cannot quite understand how this works, but
'at' is present in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
The remaining letters 'cure' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Another definition for cut rate that I've seen is " At reduced price".)

I've seen this clue in the Evening Standard.
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