Wash and dry the carp. Cut lengthwise, halving the tail fin as well. Then halve each half again. (You can keep the halves whole if your pan or deep fryer is large enough.)
Season the fish with salt and pepper. Dip the fish halves in beer, then dredge in flour. Repeat this process at least twice for a thicker, crispier coating.
Heat plenty of clarified butter in a large pan over medium-high heat. Fry the fish on each side until golden brown and crispy. (Alternatively, deep-fry until golden and crispy.)