No. ISAs are designed to give you a tax-free way to shelter your money from the taxman.
When you save or invest in a Cash ISA, Innovative Finance ISA or Lifetime ISA, the taxman cannot touch the interest you earn. Similarly, any gains made on investments in an Investment ISA or Lifetime ISA are also exempt from tax. This includes income tax and capital gains tax (with the exception of tax already paid on dividends from UK shares).
Remember, tax treatment depends on your individual circumstances and tax law may change in the future.