If you are legally resident in Spain before the transition period ends on 31 December 2020, you will be able to stay. You must register as a Spanish resident if you want to stay in Spain for more than 3 months. Children must also be registered with their own residency document.
If you are living in Spain before 1 January 2021 and register as a resident after 6 July 2020, you will be issued with a biometric residence card called a Tarjeta de Identidad de Extranjero (TIE). This card will prove your rights under the Withdrawal Agreement.
If you registered as a resident before 6 July 2020, you will have a green A4 certificate or credit card-sized piece of paper from Extranjeria or the police. This is still a valid document and will prove your rights under the Withdrawal Agreement, including after the transition period ends.
You can exchange your paper residence document for the new TIE but you are not obliged to.
The green paper residence certificate and the new biometric TIE card will continue to be equally valid in proving your residence status and rights in Spain. But, the Spanish government advises that the biometric card is more durable and may simplify some administrative processes.