You could either use an actual mask on your timer-circle layer or set the blend mode of Layer 1 to Screen. Black disappears in Screen mode, but you'll still get the clipping effect.
Either of these will work.
To clarify, an actual layer mask (
Layer > New > Layer Mask or click the "Add a layer mask" icon at the bottom of the Layers Panel) is an extra channel you add to a specific layer or layer group. It can be a "regular," pixel-based, mask or it can be a vector mask using vector outlines. In either case, the mnemonic is "Black conceals, white reveals" -- what is white in the layer mask makes the layer pixels visible, what is black makes them invisible (fully transparent). Shades of grey partially hide the layer pixels.
If you add a default layer mask using
Layer > New > Layer Mask > Reveal All, click on the mask icon to make it active, then paint on the mask with a black brush, the areas you paint over will disappear in the layer.
Masks can also be used to hide ("mask out") areas of an adjustment layer that you don't want to affect layers below. A common use of this is the familiar "colored object in a black and white photograph," where a layer mask is applied to a black and white adjustment layer to mask out the effect in one localized area.
The whole subject of layer masks and their siblings, alpha channels, is extensive. Entire sections of Photoshop "How-To" books are devoted to them. Clipping "masks" should really be termed "clipping layers," to avoid confusion of terminology. Both clipping layers and layer masks have their different uses; although there's some overlap, in most circumstances it's much more efficient to use one rather than the other.
There are probably >1k video tutorials out there, so if you search "Photoshop layer masks" on YouTube you're bound to get plenty of choices.