The FCDO has confirmed that the Spanish Government will continue to recognize until 31 October 2021 the UK driving licences of British nationals who were resident in Spain before the end of last year, even if the TIE was issued after the end of the Transition Period. This extension applies whether you the intention to exchange the licence was registered with the DGT before 30 December 2020 or not. Please note that if you arrived after 1 January, your licence will only remain valid for six months from your arrival in Spain.
This does not affect the current arrangements for driving licence exchange. If you did not register to exchange your licence with the DGT before 30 December 2020 and wish to exchange your UK driving licence now, you would need to follow the DGT process for non-EU nationals, which includes taking a driving test. There are bilateral talks, however, about the possibility of some kind of future arrangements to exchange UK driving licences without taking a Spanish driving test but at present there is no further news about that.
For the latest information on driving in Spain, please sign up for alerts to gov.uk/livinginspain and the Spanish Government’s announcement about adopting these adaptation measures to avoid disruption as the UK transitions to a wholly third country, in English, is HERE.