There seems to be a lot of confusion about the impact of Brexit and some of the preceding posts are mixing up factors which are Brexit related with things that have absolutely nothing to do with the UK leaving the EU.
I've had a try at explaining some of this before, but admittedly not on this particular forum, so here goes...
Firstly, easyJet Europe (Austria), Ryanair UK, Wizz Air UK, Aer Lingus UK etc were set up entirely as a result of Brexit. Post-Brexit, easyJet cannot use their UK AOC to fly EU-EU sectors (regardless of where the aircraft and crew are 'based' - whatever that means!). Likewise Ryanair, Wizz etc cannot use an EU AOC to fly between the UK and a point outside the EU, or operate UK domestic sectors.
Ryanair's Maltese and Polish subsidiaries, and indeed the plethora of Malta AOCs set up by other EU operators, are nothing to do with Brexit, but purely to reduce costs.
Taking the Iberia question above, there is nothing to stop Iberia 'basing' aircraft in the UK (so that the first sector of the day is UK-EU and the last sector EU-UK). Plenty of operators do that anyway in order to operate an early morning departure to their main hub. Another example of a European operator basing aircraft in the UK is Polish charter airline Enter Air who have based an aircraft at Gatwick for many summers to operate charter flights for smaller UK tour operators. Brexit hasn't changed their right to do this.
In the post-Brexit world, traffic rights are determined purely by the nationality of the operator and the origin and destination of the route, not by where the aircraft is nominally based, if that can even be determined.
As far as the TUI/Enter Air JV is concerned, I believe Fly4 Airlines was set up because TUI was rather dissatisfied with the reliability of some of their previous ACMI providers, and wanted to have more direct control over the aircraft that are wet-leased in for the summer season. As far as what is and isn't allowed since Brexit, there is no difference between TUI Airways wet-leasing aircraft from an Irish AOC holder and a Latvian, Lithuanian or Slovakian one.