I have been experimenting with Karlach and a Heat build, as she has innate fire resistance. However I often encounter this when trying to use the Heat for extra fire damage.
Casting spells is blocked.
She does not have an effect which blocks spells such as silence. She just has Bull's Strength, Blessing of Selûne, Pixie Blessing, Rage, and Bless.
So what's blocking her spell casting?
Sorry about the screenshot quality, that's HDR for you