Hi jami,
You do have the option to pay voluntary Class 3 National Insurance for the tax year you arrived officially in the UK to make it a full qualifying year. Please contact the National Insurance helpline to discuss this.
If you have access to a Personal tax account, you can also use the webchat services.
National Insurance: general enquiries
Number - 0300 200 3500
Overseas - +44 191 203 7010
Open - Monday to Friday: 8am to 6pm, Closed on Saturdays, Sundays and Bank Holidays.
Thank you.