Hi Jin Lee,
You will need to complete a 22/23 tax return at some point after 5 April 2023, including the residence section, to claim split year treatment.
Any income or gains arising in the UK are taxable in the UK.
You would need to declare this income and tax deducted on the self assessment tax return, claiming personal allowances, so that any overpaid tax can be repaid to you.
You can register for self assessment at (Register for Self Assessment