Yes, stocks and shares ISA providers allow you to transfer your investments from one provider to another. You might, however, want to first confirm whether the stocks and shares ISA accepting the transfer-in is be able to accept and handle all your open trades. You are also discouraged from initiating the transfer by way of withdrawing from one ISA provider and depositing in the next as this is considered double investment and not covered by tax exemption rules. Instead, provide your provider with the transfer details and have them initiate the transfer. They will probably charge exit/transfer fee but your investment remains protected by the tax-free rules. You cannot have more than one stocks and shares ISA provider in any one tax year. However, you can have a different provider from year to year, and you can have a different one for a cash ISA, assuming you haven't used up your £20,000 allowance with your existing stocks and shares ISA provider.