Hi,
A business which is VAT registered and making taxable supplies are required to charge VAT and account for the VAT to HMRC.
If your supplier was waiting for their VAT number to be issued by HMRC then they should have been have charging VAT during this time and there is guidance for suppliers who are in this situation.
Please see the guidance below:
Who should register for VAT (VAT Notice 700/1): 5. Accounting for VAT
As they provided a service to you with a tax point after their Registration date they are required to account for the VAT on this supply.
However the decision as to whether you make this additional payment is your decision.HMRC only require the VAT to be accounted for by the supplier and so the requirement to pay the supplier will be a dispute between your supplier and yourself.
Thank you.