Clapham started his career as an apprentice at Cambridge University Press, having already built his own makeshift press.

From Cambridge, Clapham moved to Bradford printer Lund Humphries. And in 1938 he became manager of Kynoch Press in Birmingham, before it was taken over by ICI, where he eventually became director. During the war, while investigating the metal photo-engraving screen, Clapham "accidentally invented" the isotope diffusion barrier, later to be used in the making of the atomic bomb.

As president of the IoP, Clapham also supported the Type Museum in south London. In 1996 he published Perishable Collections, a book of his life as a printer.