You can use the <animateMotion>
element.
Example adapted from MDN:
<svg viewBox="0 0 200 100" xmlns="http://www.w3.org/2000/svg">
<path id="path" fill="none" stroke="lightgrey"
d="M20,50 C20,-50 180,150 180,50 C180-50 20,150 20,50 z" />
<circle r="5" fill="red">
<animateMotion dur="10s" repeatCount="indefinite">
<mpath xlink:href="#path"/>
</animateMotion>
</circle>
</svg>
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