A new and distinct variety of Climbing rose plant, herein referred to by its cultivar name, ‘;Overedclimb’;, is provided which forms abundantly on a substantially continuous basis attractive, cup shaped deep red colored blossoms. Attractive, semi-glossy, medium green foliage is formed, which contrasts beautifully with the blossoms. The vegetation is vigorous and the growth habit is very bushy and climbing. The new variety is well suited for proving attractive ornamentation in the landscape.