Can I move a sprite permanently on each animation frame?

I've set up a few animations in Unity for a 2D pixel art style isometric grid based game and am running into issues in trying to figure out how to move the sprite by a fixed amount on each frame permanently.

I have tried setting up the movement/translation in the animation itself, timed to the frame changes. This works, however, on each run through the animation, the sprite resets itself to its original position in the first frame which defeats the purpose of what I'm trying to achieve.

I'm basically looking for a way to move the sprite's position in the world permanently by a fixed amount on each frame tick. Ideally, I'd like to to this as part of the animation I've set up in Unity and not somewhere else in code.

Is there a solution that can help me achieve the result I'm looking for (ideal solution) or are my hands tied and I'll have to handle it separately somewhere else in code (less ideal solution)?

Any help on this would be greatly appreciated.