A Solid little Piece

I would suggest what's been suggested by CarpeDraco already.

polishing a face or two and buff them to a shine.

To do so, all you need is sanding paper from fine to super fine. if you have any jeweller grade sanding paper I'd recommend them but only use such you won't use for metal later, since this is a resin it sticks in the tools.

Either hold the piece and sand them down like you would use a file, or put the sand paper on a flat surface like a table, put the stone face down on the surface and do little circular movements, with just a little pressure.

If you start piower tooling the amber it will get too hot and start charring or melting.

once you get a fine  surface you can take a polish cloth or some polishing paste for silver and rub the piece with to get a glossy surface.

It's all in little steps, but the tint of that amber piece is delightful!