You might still have to pay UK Income Tax, depending on what your ‘residency status’ will be in the country you’re going to (for example, if you’ll be a temporary or permanent resident).
HMRC will tell you how your tax will be affected.
You might be able to pay National Insurance while you’re working abroad, depending on where you’re working and how long for.
If you’re eligible, you can keep paying National Insurance to protect your State Pension and entitlement to other benefits.
Your circumstances change
Contact HM Revenue and Customs if your circumstances change when you’re abroad, eg if you move house or your marital status changes. You’ll need your National Insurance number.