Between 1974 and 1985, László Palácsik was a cross-country skier and biathlete for Honvéd Papp József SE. His first major achievement was in 1978, at the age of 19, when he finished 12th at the junior championship of the East Bloc countries. In both 1981 and 1982 Palácsik won the 20-km biathlon Hungarian Championship. Between1979-84, he won eight more team championship titles in cross-country skiing and biathlon. From 1977-85, Palácsik was a member of the national team. He took part in the 1984 Sarajevo Winter Olympics, where he was the member of the 4 × 7.5-km biathlon relay finishing 14th. After the end of his sporting career, Palácsik ran a grocerybusiness.