It depends on the type of claim you are trying to make.
Tax rebate claims for work expenses (like tools or mileage) are only applicable to lapsed (or past) tax years, except if you are making a claim because you are leaving the UK. This means you would have to wait until the end of the current tax year to be able to claim any overpaid tax. This is because the UK tax office first needs to reconcile your tax position – the tax you were charged versus what you actually paid – before deciding if you are due a tax rebate.
A tax year runs from 6th April until the following 5th April, this means that if you wish to claim a tax rebate for this current tax year (2021/22), you would have to wait until 6th April 2022, at the earliest.The exception to this is if you are making a tax rebate claim because you are leaving the UK. If you intend to claim back any overpaid tax because you’re leaving the UK, you do not have to wait until the end of this current tax year (2021/2022), which is 5th April 2022. Your claim is then considered as an “in-year” claim. Provided you have a P45 from your last UK employer, you can claim a tax rebate for this current tax year.