A shroud assembly for a gas turbine engine comprising: a shroud support that extends arcuately about an axis ; a plurality of shroud segments that are attached to the shroud support and that are arranged annularly about the axis at different circumferential positions with respect to the axis , the plurality of shroud segments including a first shroud segment and a second shroud segment , an inter-segment joint defined circumferentially between the first and second shroud segments , the inter-segment joint including a leading edge and a trailing edge that are separated apart along an axial direction; a cooling flow path cooperatively defined by the shroud support and the first shroud segment , the cooling flow path including an internal cooling passage defined within the first shroud segment , the cooling flow path including an outlet chamber configured to receive flow from the internal cooling passage , the outlet chamber defined between the first shroud segment and the shroud support and fluidly connected to the inter-segment joint ; and characterized in that a seal arrangement that extends across the inter-segment joint , the seal arrangement including a first sealing member and a second sealing member ; wherein, at a first portion of the seal arrangement , the first sealing member and the second sealing member overlap and are in abutting contact; wherein, at a second portion of the seal arrangement , the first sealing member and the second sealing member are separated apart at a distance; wherein, at a third portion of the seal arrangement , the first sealing member and the second sealing member overlap and are in abutting contact; wherein the second portion is disposed between the first portion and the third portion and defines a seal chamber that is enclosed, the seal chamber disposed proximate the trailing edge and spaced apart at an axial distance from the leading edge . a shroud support that extends arcuately about an axis ; a plurality of shroud segments that are attached to the shroud support and that are arranged annularly about the axis at different circumferential positions with respect to the axis , the plurality of shroud segments including a first shroud segment and a second shroud segment , an inter-segment joint defined circumferentially between the first and second shroud segments , the inter-segment joint including a leading edge and a trailing edge that are separated apart along an axial direction; a cooling flow path cooperatively defined by the shroud support and the first shroud segment , the cooling flow path including an internal cooling passage defined within the first shroud segment , the cooling flow path including an outlet chamber configured to receive flow from the internal cooling passage , the outlet chamber defined between the first shroud segment and the shroud support and fluidly connected to the inter-segment joint ; and characterized in that a seal arrangement that extends across the inter-segment joint , the seal arrangement including a first sealing member and a second sealing member ; wherein, at a first portion of the seal arrangement , the first sealing member and the second sealing member overlap and are in abutting contact; wherein, at a second portion of the seal arrangement , the first sealing member and the second sealing member are separated apart at a distance; wherein, at a third portion of the seal arrangement , the first sealing member and the second sealing member overlap and are in abutting contact; wherein the second portion is disposed between the first portion and the third portion and defines a seal chamber that is enclosed, the seal chamber disposed proximate the trailing edge and spaced apart at an axial distance from the leading edge . <EOS>