Smith was born into a sporting family. His father, Mansfield Smith, was a club cricketer and later a prominent sports administrator, while his older brother, Wendell Smith, also played cricket for Bermuda. Another brother, Ray, was an all-round sportsman best known as a boxer, serving as Bermuda's middleweight champion for a period. A former Bermuda under-19s player, Clay Smith made his senior debut for Bermuda in 1991, playing against a touring team from India's Hyderabad Cricket Association. He was selected for his first international tour the following year, when Bermuda toured England. At the 1994 ICC Trophy in Kenya, Smith played in all nine of Bermuda's matches, scoring 391 runs at an average of 55.85. Only two players (teammate Dexter Smith and the Netherlands' Nolan Clarke) scored more runs, while Kenya's Maurice Odumbe scored the same number as Smith (at a better average, however). Smith's highest score was an innings of 108 in Bermuda's semi-final loss to Kenya, while he also scored 89 against Ireland, 71 against the United Arab Emirates, and 51 against Denmark.