Then all treaties the UK is part of with the EU cease to apply
The Treaties shall cease to apply to the State in question from the date of entry
into force of the withdrawal agreement or, failing that, two years after the
notification referred to in paragraph 2, unless the European Council, in agreement
with the Member State concerned, unanimously decides to extend this period.
That includes things like the treaties that allow planes to fly between the UK and EU, or the UK and the U.S (as the treaties covering that are between the EU and US)
Even overflights of EU by UK will struggle - Chicago allows them, but will EU air safety recognize the UK's CAA
There have been various platitudes about how neither side wants this to happen, but not very clear how legally it will happen.