He's Lord Tarly. In the Council, he's still wearing his old clothes because they're the clothes he's got. Later, in the meeting with Tyrion, he's wearing whateverthefuck he wants to, but while they're robes, they're not a Maester's robes.
Sansa doesn't have a "Queensguard". Also, Sansa's just fine and doesn't need Brienne's protection any longer; Brienne's oath was fulfilled. Leading the Kingsguard is a nice capstone for Brienne's arc.Why is Brienne in Bran’s Kingsguard instead of Sansa’s Queensguard?