Robolectric can be used with Kotest through the RobolectricExtension which can be found in kotest-extensions-robolectric module.

To add this module to project you need specify following in your build.gradle:

testImplementation 'io.kotest:kotest-extensions-robolectric:<version>'

With this dependency added you should add extensions to your project config. For example if you have no such config yet it would look like

class MyProjectLevelConfig : AbstractProjectConfig() {
override fun extensions(): List<Extension> = super.extensions() + RobolectricExtension()

Of course you can just add this extension to another extensions you're already using.

After that done any class which should be ran with Robolectric should be annotated with @RobolectricTest annotation.