Verity was born in Leeds and, from an early age, wished to play cricket for Yorkshire. After establishing a good reputation in local cricket, he signed a contract as a professional cricketer playing in the Lancashire League. His first season was not a success but, after moving clubs, he began to make a name for himself. Initially a medium-paced bowler, he switched to bowling spin in an attempt to secure a place in the Yorkshire team. When Wilfred Rhodes, the incumbent Yorkshire left-arm spinner, announced his retirement, Verity had a successful trial in the team in 1930, and led the national bowling averages. In 1931, his first full season, he achieved the rare feat of taking all 10 wickets in an innings, against Warwickshire; the following year, he again took all 10 wickets, against Nottinghamshire, while conceding just 10 runs. The latter bowling figures remain a record in first-class cricket for the fewest runs conceded while taking all 10 wickets. He established himself as part of a strong bowling unit, which assisted Yorkshire to the County Championship seven times in his ten seasons with the club. In that time, Verity was never lower than fifth in the bowling averages and took over 150 wickets in every year except his first.