There is provided a dynamic sealing assembly for a rotary machine, comprising a primary sandwich plate, a secondary sandwich plate and a bristle pack. The primary sandwich plate comprises a plurality of primary vane openings, and the secondary sandwich plate comprises a plurality of secondary vane openings. The bristle pack comprises a plurality of bristles and is disposed between the primary sandwich plate and the secondary sandwich plate. Each of the plurality of primary vane openings overlies and aligns with a respective secondary vane opening to form a vane channel for receiving a vane along a longitudinal axis of the dynamic sealing assembly. The bristle pack is configured to: provide a brush seal between each vane received within the respective vane channels and the dynamic sealing assembly; and allow relative movement between the dynamic sealing assembly and the vane received within each vane channel along the longitudinal axis.