If the bottom of the clear running stream is clean, you have a chance that the carp may be satisfactorily edible. Give it a try and let us know.
As you may know, carp were originally brought to this continent from Europe specifically as food fish. They certainly disappointed American tastes, probably because our warm lakes and streams have skanky mud bottoms, ruining the quality of their meat.

Discard the darker meat along the lateral line that is sometimes called a mud vein. And, watch out for bones. Carp are bony.