Carol E:Are there any insurance companies who will give discount for a driver who wants to insure her first ever car in her own name, has 36 years of accident free driving and no claims, but who has always been a named driver on ex-husbands policy?

Dear Carol E

Yes there are insurers who will give discount on that basis.  When you input your details the fact that you have such a long period of driving experience will automatically prompt some insurers to give you an introductory discount.

Try running it through Moneysupermarket to see what prices are available.  You could also try E-car insurance.