You would either have to become self employed and complete a tax return. HMRC would then bill you annually for tax and NI; or, set up a company for your new employer to engage with; or, join a contractor umbrella company.
Beware however of only working for a single ‘customer’ if you set up as a company. HMRC may treat this as ‘concealed employment’ under a rule called IR35 which has serious tax implications. This can be quite complex. There’s more information here:
https://www.hiscox.co.uk/business-bl...tors-hiscox-uk