Does ESET run on Linux?

ESET Endpoint Antivirus for Linux exists and supports Ubuntu, Red Hat, Debian and SUSE, but it is sold as part of ESET's business range and is deployed through their management console. It is not something a home user buys for one laptop, and your consumer licence does not cover it.

So in practice, for someone switching a home computer, the answer is that ESET does not come with you. Your existing licence still covers any Windows or Mac machine and any phone in the household, so check what else it applies to before you let it lapse.

You will most likely not need a replacement. Linux installs software from a checked app store rather than from downloaded installers, and asks for your password before anything can change the system, which removes most of the routes home malware takes on Windows. Running no antivirus is the normal choice here, not a reckless one.

If you do want a scanner, usually because you still handle files for Windows machines, ClamAV does that job and costs nothing. It checks files on demand rather than watching everything in the background.