A barley cultivar, designated Claymore, is disclosed. The disclosure relates to seeds, plants, and derivatives of barley cultivar Claymore, and methods for producing a barley plant by crossing barley Claymore with itself or another barley variety. The disclosure also relates to barley varieties or breeding varieties and plant parts derived from barley Claymore, to methods for producing other barley varieties, lines, or plant parts derived from barley Claymore, and to the barley plants, varieties, and their parts derived from the use of those methods. The disclosure further relates to hybrid barley seeds and plants produced by crossing barley cultivar Claymore with another barley cultivar. The disclosure relates to methods for developing other barley varieties or breeding lines derived from variety Claymore, including cell and tissue cultures and haploid systems.