He started his playing career while serving the mandatory military conscription and affiliated in the Yugoslav Navy side Mornar Split, later moving to Yugoslav Air Force side FK Naša Krila Zemun.
Partizan was newly formed club which gathered most of the best players of the country, so Tapiška found himself in difficulties to establish himself, despite all, he managed to make with Partizan one appearance in the 1946–47 Yugoslav First League, 4 appearances in the Yugoslav Cup, and 29 in friendlies and tournaments.
[1] Not wanting to stay as a substitute, Tapiška decided to leave Partizan and joined FK Spartak Subotica where he spent the next 14 years.
Tapiška retired in 1960 and in his honor Spartak organised a farewell match against Dynamo Dresden.
[2] After finishing his playing career, he became a manager, and coached minor local teams such as Vonogradar and Zorka.