The present invention relates to an assembly for a turbomachine turbine extending along an axis (X), comprising: —an ejection cone (100) comprising a radially outer annular wall (102) defining a flow duct for a flow of hot gases and a sound box radially arranged inside the outer annular wall (102), the sound box comprising a radially inner annular wall (104), —a connecting member (106) intended to be axially inserted between the exhaust housing and the ejection cone (100), the connecting member (106) comprising an upstream annular flange (108) intended to be attached to the exhaust housing and a plurality of downstream securing tabs (110) connected to the inner annular wall (104), —an annular sealing shroud (112) comprising an upstream portion surrounding the securing tabs (110) of the connecting member (106) so as to cover the spaces circumferentially located between the securing tabs (110) and axially located between the upstream annular flange (108) of the connecting member (106) and the radially inner annular wall (104).