Cleaver first started contributing illustrations to the Graphic from 1887. In 1890, he joined the newly launched Daily Graphic (the first illustrated daily newspaper) and quickly established a new school of pictorial news reporting. He also contributed to Pearson's, Strand, and Punch (1891 – 1937). A specialist in parliamentary scenes for his illustration work on the Daily Graphic, his cartoons were mostly of a social nature. James Thorpe, in his book The Illustrators, called him 'an accurate draughtsman with great mastery of the pen, a clean, sure, open line, a great gust of portraiture and a sense of humour.'