[4] In late 1973, Tapper had the chance to win his first major event at the three-round Hibiscus Coast Classic.

He won a number of minor tournaments across Australia in 1975,[7] including the Bankstown pro-am by two over Peter Kohlsdorf.

Marty Bohen, who was in second place, had a chance to take the clubhouse lead but bogeyed the final hole to fall into a tie with Tapper.

Jones, the leader all day, had a weak final round and then double-bogeyed the 18th to fall into a tie with Tapper and Bohen.

Tapper was one back of Bohen entering the 17th hole but made a 14-meter eagle putt to tie the American.

[10] This performance would help him earn the Most Improved Player award by the New South Wales Professional Golfers Association in February.

[13][14] He also finished third at that season's Queanbeyan City Open's pro-am, the site of one his best placings on tour, two behind Peter Kohlsdorf.