The following assumes you're in the UK. First, you should ensure that your second employer informs the tax office that you have started work, and obtains a tax code for you. If necessary, you should contact the tax office yourself, and discuss your situation with them. However, I think you will find it difficult, if not impossible, to ensure that you pay the correct amount of tax during the current tax year. You'll possibly underpay, and have to make it up after the end of the tax year; or, more likely, overpay and have to claim a refund.