Glass object but no alpha??

It looks like you have Opacity set to 1. That will "lock in" whatever shows in and on the glass, so that it will be fully opaque in Photoshop.

There are two key properties related to transparency. One is Opacity, in the Base Surface properties (the key word is "Surface"), and the other is Translucency, in the Interior properties. If Translucency is set to 1 (full translucency) and Opacity is also set to 1 (full surface opacity), you will see through the glass material in the viewport, but the environment will be fully reflected from the surface everywhere there is no object, like this. I've rotated the environment light to make it obvious. This is what you get if you use the default Glass material at the top of the Starter Assets, because surface opacity is set to 1.

When this renders out, the glass is opaque. If it showed a background color, that would be opaque. This is quite different from what you would see in real life, so it's counter-intuitive. In my view, it's wrong, but there it is.

With Opacity adjusted to 0.15, this appears in the viewport:

Notice that you can see the background through the glass. It is also transparent in the PSD render.

Opacity and Translucency are a little bit like Opacity and Fill in Photoshop. You can think of it this way: Opacity determines whether you can see [the surface of] the object at all, and Translucency controls whether you can see through it.

In this image, an interior title page for an article in CreativePro Magazine, notice that the tail of the "Y" is visible through the windshield of the car. I added the article title in Photoshop. The glass material in the sport car model uses Translucency and a low Opacity, so I didn't have to do any additional adjustments in Photoshop.

I hope that's useful. Spend some time playing back and forth between these two properties to get a feel for how they interact. It's not intuitive.

I think you need to change translucency values  of that glass.