Apap was born in Valletta on 16 April 1919. From a very young age he started following different sport events. He was a committee member of the Ta' Xbiex Waterpolo Club, the Valletta United Waterpolo Club, the National Sportsmen of the Year, the Malta Boxing Association and the Malta Pool Association.
He organized a number of popular competitions, including canoe races, football games, tug-of-wars, professional wrestling matches and athletics. Willie Apap also organized the popular Strong Man Acts and endurance swimming challenges, during which, Albert Rizzo and Alfred Kitcher broke world records. He also introduced American Poll (the 8-Ball Game) in Malta.
Although he was born in Valletta, Willie Apap spent most of his life in Gżira. He was one of the founders of Gżira United FC and was appointed Honorary Club President in 1990. He was also a member of the Gżira Local Council.
He died on 12 June 2004 at the age of 85.