To be pedantic, Scottish homeowners haven't paid 'rates' since 1989, when the Community Charge was introduced. That, in turn, was replaced by Council Tax in 1993.
When a property is sold, it's Council Tax band will remain unchanged
unless improvements have been made to the property by the previous owner.
If, for example, the property your daughter is interested in was in Band A when the existing owner bought it, it will remain in Band A when she purchases it as long as it's not been improved.
However if the existing owner has added a dormer loft conversion, an extension to the side, a conservatory at the rear and an indoor swimming pool, he/she will have continued to pay Band A Council Tax after those improvements were made but the property would then, almost certainly, be placed into a higher band after the sale has gone through (with the assessor having to estimate what the value of the improved property would have been in 1991).
https://www.saa.gov.uk/council-tax/