Remove any furniture from the area. Spread out tarps over the floor under the new wall.
Brush primer around the edges of the new wall with a paintbrush in a thin, even coat. Roll primer over the rest of the wall with a paint roller. Let the primer dry 12 hours.
Brush your textured paint along the edge of the wall that abuts the other textured wall. Match the style of the texture, working the surface with the brush as needed. Step back and assess the two surfaces, old and new, from a slight distance to get it right.
Apply textured paint over the rest of the edges of the wall with the brush, then do the middle with the roller. Stop frequently to step back and assess the texture, making sure it's consistent with the older wall.
Let the new paint dry for 24 hours before bringing back the furniture.