You need to get a BRP within 6 months upon arrival, but it's better to do it as soon as possible, as it will make a lot of things much easier. If you submitted your biometric data before entering the UK, then you will have received a visa confirmation letter with an address where you can pick up your BRP. You'll need to pick it up in about a week after your arrival and have your passport with you.
If you did not submit your biometrics to get in the UK, you will need to do the following.
- Fill in the form: https://apply.visas-immigration.service.gov.uk/product/ukraine-scheme-brp . It is very similar to your visa application, the only difference is you'll need to state that you are in the UK. You will need only your passport.
- You will be asked to pick a biometric collection centre closest to you and submit your biometric information. It may say you'll need to pay, but do not worry: the Ukrainian visa scheme provides BRPs free of charge. You can choose to pay for premium services to get it faster, but it's not usually worth it. Choose a center closest you. The centres are very busy, so the nearest date may be a week or more away. Don't be late because you can lose your slot and have to start over.
If something has changed before you received BRP or after, you can request a change here https://www.gov.uk/change-circumstances-visa-brp.