A bit obvious, or desperate, but the Royal and Ancient at St Andrews , Fife,KY16 9JD should be able to help.
They must have access to records of golf clubs and courses, both current and disappeared. They have a big library and quite an archive.
Failing that, there's bound to be a County Archivist for Norfolk, lurking somewhere in the bowels of a building in Norwich**.
Sandringham itself, the Christmas retreat of Her Majesty (not sure why, unless they go for a bit of shooting. It was built as a hunting lodge

) might help one of us, her subjects, assuming always that the course was on part of the Sandringham Estate. That seems quite likely, from what you say. The family have not been enthusiastic golfers, though one of their current younger members was President of the R and A, so it's no surprise that the course was never reinstated postwar when others, similarly treated, were.From the date and era when it was flourishing, we might surmise that the course was designed by the fashionable James Braid, as was the Gog Magog in Cambridge (now there's an irrelevant guess !).Golf courses in this region seem to date from quite a narrow period at the end of the C19/early C20, though Royston G.C, Herts, claims to have a site used by James I.
** Yes, there is. It's Dr Alban,there is a website to be found by keywords 'County Archivist Norfolk' which offers online searches, and the office is at Norfolk Records Office, The Archive Centre, Martineau Lane, Norwich,NR21 2DQ.