During Texas’s period as a sovereign Republic from 1836-1845, it acted as a sovereign nation would, by sending diplomats to other countries. In fact, there is a marker in London signifying where Texas’s delegation resided.
The republic was recognized by the governments of France and Britain, which were interested in the fledgling nation for reasons of trade and international gamesmanship.
Texas had an office on the Place Vendome in Paris. In London, the Texas legation was near St. James’s Palace. Its location is marked today with a plaque that reads: “In this building was the legation for the ministers from the Republic of Texas to the court of St. James, 1842-1845.”
So if Texas does secede from the Union, there will definitely be a place to reside while sending a delegation to the Queen’s court.