Here is an example SVG with a clipping path made in Illustrator. It's basically some straight lines which have been grouped, and a circle applied as a clipping path. There is no problem here. The SVG works fine in browsers. There is nothing you need to do except export as SVG. There is no need to expand anything. The SVG format supports clipping paths.
If your issue is that the SVG isn't displaying properly in Figma, then the problem is with Figma. After trying the above SVG in Figma, it doesn't appear to support this feature properly, or it may be a bug. It doesn't even import the clipping path vector. This may be a result of Figma's masking being quirky - it's upside-down.
So, with that in mind, here's workaround for dealing with clipping paths for use in Figma.
In Illustrator*, release the clipping path using Object > Clipping Mask > Release.
Select the clipping path and change the fill to black, no stroke.
Export the SVG
Import the SVG into Figma
In Figma, in the Layers panel, move the artwork group above the vector to be used as the mask, i.e. Artwork group on top, and vector to be used as the mask directly underneath (this is the quirk I mentioned above)
Select the group and the vector to be used for masking, and click Object > Use as mask
*Note: For those who don't have access to Illustrator, this fix will also work using other software such as Inkscape (which is free and Open Source). In Inkscape the equivalent operation is Object > Clip > Release. To export for Figma, use File > Save As and choose "Plain SVG" or "Optimised SVG" as the file type.