After December 2020, UK Citizens will be Third Country Nationals, that much is fact. There is no “future movement” in the current trade discussions, so even if or when a deal is struck, UK Citizens still become Third Country Nationals. Spain has confirmed that.
There is NO “special arrangement” for UK Citizens seeking to move to Spain.
Having got that out of the way, you may well be a little confused as to what the “new” method will be - this is a step-by-step blog post from an American who outlines the process for a Third Country National that should be looked at by anyone coming over post 2020. In particular the need to get your Visa first, which appears to allocate your NIE number, then arrive within 3 months of receiving visa, and apply for TIE within 30 days of arrival. It’s dated 14th October 2019, so still pretty relevant. The procedure outlined here will very likely be the one you follow, as post 2020 there are zero differences between a US Citizen and a UK Citizen in terms of ability to move to Spain.
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https://www.wanderingearl.com/spanish-residency-card-tie-all-you-need-to-know
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