Clennell was born in New Silksworth and began his career with Blackpool in 1910. He was top scorer for the "Seasiders" in 1910–11 scoring 19 goals which attracted the attention of First Division clubs. Blackburn Rovers signed him in April 1911 and in his first full season at Ewood Park he won a First Division champions medal. Injuries restricted him to few appearances for Rovers and he joined Everton in January 1914 when he again won a First Division in 1914–15 where Clennell scored 14 goals. His career was interrupted by World War I but he resumed playing for Everton in 1919. He spent two more seasons at Goodison Park before leaving for Cardiff City in October. He was a very useful forward for the "Bluebirds" and very nearly helped them win the title in 1923–24 but they agonisingly missed out to Huddersfield Town on goal average. He then played two seasons for Stoke City scoring 9 goals in 35 matches and ended his career with Bristol Rovers and then Rochdale.