when unwrap image for iris, the UV mapping not on the exact location of the iris.
The process of UV mapping is exactly trying to match the 3D space cooridinates of the mesh to a 2D space texture. Blender doesn’t automatically recognize the color data from your image and try to fit the vertices into that data. It’s the users task to do the mapping.
So you need to move the vertices (all) on the right hand side to match the texture with color data. This is called UV mapping.
One suggestion to make that easier, when you rendered the iris image you could have used square image instead of a rectangular one. So rendering the iris, say, in 1024 x 1024 you would not have this problem since your whole vert data would “fit” inside the iris render (diffuse image). Plus it looks like you have some surplus space on the top and bottom of the iris. Position the camera so that it fills the whole render and this becomes much easier.
Hope this helps!