Updating a UV map

So I’m trying to texture an iris. At the moment. For some reason the texture in the viewport isn’t picking up on the fact that I’ve adjusted the vertices in the UV editor to encompass the blood vessel almost all the way around. See what I mean?

I’m a real noob at texturing so am wondering if theres something I’ve got to reload or update to get this working?

What if you add default checker texture at first and look at the stretching which is probably going on? Quads need to be approx equal size imo.