If you are living abroad the first step for you to apply to pay voluntary National Insurance contributions and to find out which rate you would be eligible to pay (class 2 or class 3), would be to complete an application form CF83.
You can find this here:
Social Security abroad: NI38
This leaflet provides all the information you need and the CF83 is at the back of the leaflet. It needs to be completed in full and posted to HMRC at the address shown on the leaflet.
If you have any queries about completing the application form, you can contact HMRC here:
National Insurance: non-UK residents
Before deciding to pay voluntary National Insurance contributions, we would also advise you to contact the Future Pension Centre at DWP to confirm if paying voluntary National Insurance contributions for certain years will actually increase your pension.
Contact the Future Pension Centre
You can find guidance on contracted out queries here:
Contracted out of the State Pension
This explains what contracted out is, which is when your employer deducts class one National Insurance contributions at a lower rate. The Future Pension Centre will also be able to explain how paying at the contracted out rate has affected your UK pension entitlement.