Extract from :
https://www.lamoncloa.gob.es/lang/en/brexit/howtoprepare/Paginas/190108residence.aspx
UK NATIONALS OR THEIR FAMILY MEMBERS RESIDENT IN SPAIN AFTER THE DATE OF WITHDRAWAL
1. What will my situation be?
The Withdrawal Agreement provides for a transition period to be established lasting from the withdrawal date to 31 December 2020. This period may be extended.
During this transition period UK nationals and their family members resident in Spain who are nationals of non-EU countries will maintain their rights derived from the application of EU law (except for the right to vote and stand in elections to the European Parliament and the right to use the EU Citizens Initiative).
Once the transition period ends, the Withdrawal Agreement stipulates that your rights of residence, work, study and social security will be maintained.
You have to bear in mind that the registration certificates (the green certificate) and ID cards of family members of the EU citizen obtained before the end of the transition period will subsequently serve to accredit their legal residence in Spain and benefit from the provisions of the Withdrawal Agreement. However, the Spanish government is working together with the European Commission to have a Foreign Identity Card that explicitly mentions your condition as beneficiary of the Withdrawal Agreement. The procedure for processing this card in the coming months will be completed soon.
Having a registration certificate in force is a guarantee of your rights as resident in Spain.
You can consult this European Commission document, which includes questions and answers on who benefits from the Withdrawal Agreement and what their rights are.
The rights of British citizens and their family members who begin their legal residence in Spain after the transition period will be those established by the agreement regulating future relations; if there is none, the general arrangements governing foreign residents in Spain will be applicable.
2. I have a registration certificate. Can I continue to reside in Spain?
Yes, you may continue to reside in Spain. Both registration certificates – green certificate – and EU citizen family cards obtained before the end of the transition period, will serve to prove your legal residence in Spain at a later date and benefit from the forecasts of the Withdrawal Agreement.
In addition, both you and your family members may request a Foreigner Identity Card to be issued explicitly mentioning your condition as beneficiary of the Withdrawal Agreement, which will facilitate both administrative procedures and any crossing of the external EU border. The procedure for processing this card in the coming months is being finalized.
3. What is my situation if I arrive in Spain after the withdrawal date but during the transition period (from the withdrawal to 31 December 2020)? What do I have to do?
The Withdrawal Agreement establishes a transitional period until 31 December 2020, during which the Withdrawal Agreement will apply, and therefore yours rights will be derived from the application of EU law (except for the law of active suffrage and elections to the European Parliament and the exercise of the EU Citizen Legislative Initiative).
Until the Spanish government has available the issuance of a Foreign Identity Card that explicitly mentions your condition as beneficiary of the Withdrawal Agreement, you may request yours certificate of registration – green certificate – and/or cards of relatives of EU citizens to the Offices of Foreign Affairs and Police Stations.
Having a certificate of registration in force is a guarantee of your rights as a resident in Spain.
If you already have Spanish nationality you will not have to do anything else.
4. Will UK nationals resident in Spain have to obtain a work permit to continue their professional activity in Spain?
No. The Withdrawal Agreement protects the rights of EU citizens and British nationals, as well as their respective family members, to continue living, working or studying as they do now and under the same basic conditions as under EU law. You may therefore continue to work as now without any additional permit.
5. Do family members of a UK national who are nationals of non-EU countries and resident in Spain have a special status?
Family members will retain their rights arising from the application of EU law (except for the law of active and passive suffrage in elections to the European Parliament and the exercise of the EU Citizen Legislative Initiative).
After the end of the transition period, the Withdrawal Agreement provides that your rights of residence, work, studies and Social Security will be mantained.