Hi Bob Olivier,
Depending on what you mean by non-resident you may be able to pay voluntary National Insurance contributions to the UK.
If you are overseas you can read the NI38 leaflet on GOV.UK and apply to pay voluntary NICs from abroad. If you want to apply there is a CF83 application held towards the end of the NI38 information.
Social Security abroad: NI38
If you are in the UK then there are different conditions for voluntary National Insurance contributions.
You can also contact the National Insurance team for further advice.
National Insurance: general enquiries
Thank you.