A third Renown changes modernization and deployment choices

Would completing a third Renown-class battlecruiser cancel the Admiral class, and how might it affect the Second World War fleet?

No; it would enlarge the battlecruiser force, likely shift a major modernization from Royal Oak to the extra fast ship, and change which capital ships were available for Force Z and the Bismarck hunt.

The extra battlecruiser would come from an uncompleted Revenge-class hull rather than replace Hood and her Admiral-class sisters. Britain would then possess three Renowns alongside Hood, its battleships, Nelson, and Rodney. A second battlecruiser might receive the major modernization historically given to Royal Oak, leaving two improved fast capital ships available when war began. That additional ship could replace Repulse in Force Z, accompany Hood, or join the hunt for Bismarck, so the effect emerges through refit priorities and operational assignments rather than a fixed single outcome.