Royce began his career with non-League Heybridge Swifts and after claiming the number one jersey off long standing Albie Bridge while still a teenager soon attracted the interest of many Football League sides. He joined Southend United for a £35,000 fee in October 1991 and became the first Heybridge player to be sold to a professional club. He spent a few seasons as understudy to Paul Sansome before finally establishing himself as the Shrimpers' first choice and a fans' favourite – he played in the successful Southend side in the mid 1990s under Barry Fry and later Peter Taylor before Charlton Athletic manager Alan Curbishley snapped him up on a free transfer. Despite some strong performances in the Premier League, including many clean sheets resulting in setting a post-war club record, injury prevented Royce from establishing himself as regularly as he would have liked and, after the arrival of Dean Kiely, he rejoined former boss Peter Taylor at Leicester City. Some good early form resulted with speculation about an England call-up for new manager Sven-Goran Eriksson's initial squad, however this never materialised and further injuries prevented Royce from making as many first team appearances as he possibly could. A second spell at Charlton followed before he moved into the lower tiers of the Football League with Queens Park Rangers, Manchester City, Luton Town and Brighton & Hove Albion again teaming up with Peter Taylor. During a Stoke City vs QPR game, he was attacked by a Stoke fan. Royce joined Gillingham in April 2007 as an emergency loan signing after the Kent team were left with no fit goalkeepers for their final three matches of the season, making his debut for Gillingham in the 3–2 home win over Port Vale on 21 April 2007. In August 2007 he joined Gillingham on a free transfer, saying that he intended to see out the rest of his career at Gillingham and his performances in goal won him the Supporters' Player of the Year award for the 2007–08 season. He was first choice goalkeeper at Gillingham again in the promotion season of 2008–09 and at the beginning of the following season. He was forced out of the team by injuries sustained in a car accident in December 2009 and never regained his place from Alan Julian. His Gillingham contract expired at the end of that season and although he had been offered a goalkeeper/coach role at Gillingham, he opted in June 2010 to take up the role at Brentford, where he remained until the end of the 2017–18 season. He returned to Gillingham as a goalkeeping coach in June 2019 and was listed on the bench against Oxford United due to an injury to second-choice keeper Joe Walsh. The Kent side announced in June 2020 that Royce would be released when his contract expired the following month.
