All employees pay National Insurance contributions and if you do want to work then you must apply for a National Insurance number. The National Insurance Number (NINO) is a number unique to you to which will help your employer to pay your National Insurance contributions. No one else can use this number.
"Temporary NI numbers" are no longer accepted so you must have an NI number to work. You may be able to start working without a National Insurance number but you may need to get one before you are paid. This is the case if you wish to work at the University and may be the case with your new employer. You must check with them before you start.
You can apply for your National Insurance (NINO) online in the Government website.