Your ability to pay into a UK pension very much depends upon your tax position.
If you still have UK earnings that are chargeable to UK income tax after moving abroad, then personal contributions can continue to be made into existing pension schemes as before. The limit on personal contributions for tax relief purposes would still be the greater of £3,600 gross pa and 100% of your UK earnings in that tax year subject to the Annual Allowance (combined employer and employee pension contributions) plus any unused carry forward allowances.
If you don’t have UK earnings chargeable to UK income tax on moving abroad i.e. you are are full UK expat and you are being paid and taxed overseas, you are only able to receive tax relief on personal contributions to an existing pension scheme of up to £3,600 gross pa for five full tax years following the tax year in which you moved abroad. Caveat: you must have been resident in the UK when you became a member of the pension scheme.
In short, if you are not resident and not taxed in the UK, you can only continue to pay into an existing scheme for 5 years, you cannot set up a new pension scheme in the UK and then get tax relief.
If you have a UK employer, they can continue to contribute whether you have relevant UK earnings or not.
If you fail all of the above, then you will find it difficult to set up a private UK pension scheme.
If you fail the above, you may need to seek advice locally about setting up an offshore savings/retirement savings scheme. This would need to be done by an adviser authorised in your country of residence.