In AGOT it is mentioned that part of the crown’s debt is to several Tyroshi trading cartels. What are those and how old is the word cartel itself anyway?

A cartel is a group of economic actors – either sellers or buyers – who agree to cooperate in an attempt to create an oligopoly that can fix supply and/or demand (and thus prices), market share, and so forth. A trading cabal would probably be focused on trying to control a geographic market, or on trying to corner a given commodity. 

In terms of its origin, the use of “cartel” with regards to business dates back to the late 19th century, where it was used in Germany to describe business organization in the new industries (whereas in the Anglo-American sphere, the terms “trust” or “combination” predominated).