If you pay income tax (either from investments, pension or earned income) then you should consider re-investing the proceeds from your ISA in another one. This is because interest earned from ISAs is tax-free, which effectively increases the returns by 21% for basic rate tax payers.
Even if you are not a taxpayer ISAs tend to give s slightly better rate of return anyway than ordinary investments. If you can tie your ISA investment up for a fixed term you will receive a fixed guaranteed rate, which is likely to be a considerable improvement on a variable rate deal.
You can transfer the funds from your existing ISA (either all or part) to a new provider of your choice and those funds, together with any other contributions you may make (you can invest up to £5,100 in each financial year at the moment) will continue to earn tax-free interest. However, if you withdraw the proceeds of your existing ISA the tax free status of those funds is lost and you cannot re-invest them and enjoy tax free returns.