You must obtain a National Insurance number if one is available. If the employee doesn’t have one, they must register for one as soon as possible. You can pay them and file your Real Time Information (RTI) submissions without the NI number, since it isn’t an HMRC technical requirement.
In this situation, provided that the person you are paying has the right to work in the UK, then you should use a 'holding' NI number. For example AA123456A.
This will allow you to submit payroll for these employees.
Note: it is very important to update this with the real national insurance number when you receive this as then HMRC will be able to link the salaries submitted to that individual for tax purposes.
If you file an RTI submission without an NI number, HMRC will attempt to look it up and issue the relevant NI number, if found, via an electronic RTI notice.
It is important to chase the employee for their NI number if they have one as it is imperative that you have checked they have the correct right to work.