There are various routes which may lead to permanent residency, which is also called indefinite leave to remain. In most cases, you will have to pass the ‘Life in the UK’ test and an English language test.
EU/EEA citizens can continue to apply for the EU Settlement Scheme until 30 June 2021, although they must reside in the UK before 31 December 2020. Applicants can secure either Settled or Pre-Settled status dependant on whether they have previously resided in the UK for a continuous period of more than 5 years. You have the right to live, work and study in the UK with this status, and can seek citizenship following 12 months of Settled status.