Employers often ask if you have a National Insurance number to check that you have permission to work in the UK. There are other ways of proving that you have permission to work and you can start work with no National Insurance number and then apply for one later. 

Read more on this topic at: https://www.ukcisa.org.uk/Information--Advice/Working/Employers-income-tax-National-Insurance#layer-3766 

Apply for a National Insurance number here: https://www.gov.uk/apply-national-insurance-number