It’s called a tar. It’s a long-necked lute with a skin-covered resonator used in Iran and Iranian-influenced areas (e.g., Azerbaijan). Sahba is Iranian, plays Iranian Classical music on it, although I gather she can be a bit controversial for purists. (She’s as much a composer as a performer, and that means qu’elle prend son bien où elle le trouve, which is something that doesn’t sit that well with purists anywhere.)
I have another performance of hers in the Earworms thread. Chahar mezrab is a type of instrumental movement (like sonata allegro is in the West).
Mercifully, not all of these “supergroups” always come off as overblown vanity exercises. Here’s an international one: a New Yorker, a (late lamented) Glaswegian and a Montrealer. Call it Cream meets Mountain.