It depends on when they arrived in Spain:
- Before 1 January 2021: British citizens who were already legally resident are protected by the Withdrawal Agreement (Article 50 TEU). They were issued a special "Article 50 TEU" TIE that preserves their rights as if they were EU citizens (work, reside, healthcare). That TIE is renewed, but the underlying rights are permanent.
- After 1 January 2021: they are treated as non-EU nationals (third-country citizens). They must apply for a visa and the TIE like any other non-EU foreigner, through the general immigration system.