How to spice up a carrot cake
Cayenne pepper.

I'm actually serious. I haven't tried it in carrot cake but a little capsaicin actually works well with a little sweet to offset it. Chile powder also works well in sweet things.

Cardamom is my wife's favorite and so it goes into many baked goods I make. It would work and be interesting but not spicy.

You can always put in a good extra dose of cinnamon if you want it to punch you in the face.