I am 73 years of age what is the best interest rate for my ISAS, which bank and can I transfer my existing ISAS

Hello elke, welcome.
The interest rate all depends on how long you wan't to tie your money up for. Not all providers allow transfers in so you need to look for a GREEN TICK under the heading ISA TRANSFERS IN.
Click on the link below, it will take you to a selection of Cash Isas.
http://www.money.co.uk/savings-accounts/cash-isas.htm
Remember, ALWAYS allow your "old" provider and your "new" provider to do the transfers for you, DON'T attempt it yourself or you will lose your tax free status.
Hope that all helps.