TUI UK WILL continue to fly outside of the EU whether deal or no including to the Caribbean Mexico and US .
They WILL continue to fly from the UK to the EU as well however their ownership structure may need modifying .
Its highly likely in the event of no deal and aircraft certification problems; This is a Genuine risk we will will see some migration of aircraft registrations to Germany Scandinavia and or Belgium to over come issues in the short term.
TUI Group have options here.
As an airline within tour group operating charters is far less of a problem for TUI than many.