Let's take a look at the GBHpedia entry for the current relationship between Texas and Texas A&M

Cold War

The Cold War was a state of political and athletic tension after conference realignment between powers in the SEC (Texas A&M) and powers in the Big XII (Texas, Baylor, and others).

Historians do not fully agree on the dates, but 2011 to present day is common. The term "cold" is used because there was no football played directly between the two sides, although there were many transitive victories and recruiting battles, known as moral victories, supported by the two sides.