Can I keep my Mint Mobile Sim Card?

Indeed, call Mint as recommended in all replies.

FWIW, my own U.S. MVNO isn’t on Apple’s below-linked “eSIM Carrier List” either but they DO INDEED support eSIM.

Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support (CA)

It depends on which iPhone you want to purchase and in what country you reside.

If you want the newest iPhone 14, and you live in the US, Mint Mobile would need to support eSim as iPhone 14 models sold in the US are eSim only. No physical sim.

I don't see them on the list of eSim providers on the Apple list. So you should ask them directly if they can support eSim.

Mint mobile does not currently support the eSIM. You will not be able to use an iphone 14 with their service until and unless they change that policy. Contact Mint Mobile for more information.

Assuming that you’re moving to an iPhone 14 … You need to call your carrier and ask how you can migrate your service to eSIM.