A vane assembly for a gas turbine includes a first shroud segment, a second shroud segment, a first inner air seal, and a seal assembly. The first shroud segment has a first end face. The second shroud segment is disposed adjacent to the first shroud segment and has a second end face that faces towards and is spaced apart from the first end face by a gap. The first inner air seal extends into the first shroud segment and defines a first trench. The seal assembly at least partially received within the first trench.