 In 1921, Verity made his debut for Rawdon in league cricket; some of his subsequent performances attracted the notice of the local press, and he took 29 wickets at an average of 13.80 that season. The following season, he was spotted by Yorkshire coach George Hirst and former England spinner Bobby Peel, who were talent scouting for Yorkshire, and given a trial in the cricket nets at Headingley cricket ground. Peel realised Verity was an intelligent bowler who had excellent control of where he pitched the ball, but believed he was not fast enough to be effective for Yorkshire. Meanwhile, critics in Rawdon began to see increased potential in his batting, which improved steadily; by 1924, the Yorkshire Evening Post described Verity as "one of the most promising cricketers in the Leeds district".
