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Tax relief on UK salary income
The broker that is issuing the moneys after vesting is more than likely deducting a notional amount of tax and NI based on UK income tax laws. If you are not a UK resident, then you should pay income tax on those stock options based on your own tax residency. Best thing to do is speak directly with the broker to explain the situation, ask them to not deduct anything from your stock options - but keep in mind that you will need to declare these earnings yourself and pay the correct rate of tax. From my own personal experience, the UK employer more than likely receives the net value (after the notional tax and NI have been deducted) and in usual circumstances create a tax liability on your payslip (if you were working and had earnings). If of course this deduction is being made by the employer, then you can simply ask them to correct this (most UK payroll software will automatically deduct tax and NI for payments after leaving unless manually intervened, so they probably aren't aware if it is them doing so).