Combining GIF?

You can import your animated gif as side-by-side frames in a canvas, but it wouldn't be much different from loading your original .pyxel file.

It sounds like you want to use the full animated gif as a sort of layer on top of your new animation, and have them run as separate animations in a single gif file. My somewhat hacky suggestion in this case would be to use some kind of a program/system you're comfortable with (Unity, HTML with CSS, even PowerPoint/Google Slides would probably work).  Position your three gifs in that program, then when you preview them at runtime you use Screen2Gif to capture them as a single animated gif.

I should point out, however, that if you use my hacky solution with Screen2Gif, you might have some undesirable timing if your three animations have very different loop times. If the animations don't need to be in sync with each other, then you'll be fine.

Otherwise, you're best off going back to your new .pyxel file, making a new layer for each animation's frames, importing each animation's spritesheet as a tileset, and placing the tiles in the desired tile/frame position of that animation's layer.

Hi Ellianesh

As FlyingKatsu points out, adding full animated gifs to your canvas is not possible. You will have to use another program for that. You could alternatively make your tiles wide enough to place your sprites next to each other, but in my opinion that's too much of a hassle. 

The quick and easy method in action: https://youtu.be/KMyuZSgiXnw
The more correct method in action: https://youtu.be/veetYFOBmMk