He played for Penn State from 1961 to 1963, quarterbacking winning teams each year. In 1961, he saw limited action (17 for 32 and 216 yards) but was a starter in the other years. In 1962, he completed 91 of 162 passes for 1,037 yards and 12 touchdowns (with four interceptions.) In 1963, he completed 87 of 161 passes for 1,117 yards and ten touchdowns (with five picks.)
Liske saw limited playing time in 1964 with New York, playing in only four games (only 18 passes). His career took a turn up north, with the Toronto Argonauts of the Canadian Football League. Canadian teams of this time were still a very viable career option, as they paid comparable money and offered more playing time. Liske played 11 games with Toronto in 1965.
From 1966 to 1968, he moved to the Calgary Stampeders, where he enjoyed his greatest success as a professional. In 1967, he threw for 4,479 yards, a whopping figure for that era, and 40 touchdowns, the latter breaking Tobin Rote's league record of 38 in 1960 for Toronto. His touchdown record would stay in place until Doug Flutie surpassed him in 1993. He was named an all-star and won the CFL's Most Outstanding Player Award. In 1968, after a season comprising 4,333 yards passing and 31 touchdowns (though with 28 interceptions), he led his team to the 56th Grey Cup, losing a close and exciting game to the Ottawa Rough Riders. Liske's passing records would eventually be eclipsed by Doug Flutie's in a more wide-open era.
Liske chose to return to the AFL in 1969, joining the Denver Broncos and playing seven games with them. In 1970, now in the NFL, he played 11 games with Denver. He moved on to the Philadelphia Eagles for the 1971 and 1972 seasons, playing 14 games in each season. Unfortunately, he did not enjoy the success he had in the CFL, as none of his teams had a winning season. His combined total American professional record was: 50 games over five seasons, with 396 of 778 passes completed, for 5170 yards and 30 touchdowns with 46 interceptions.
Canada beckoned once again, and in 1973 he rejoined the Stampeders. He remained in Calgary until part way through the 1974 season, when he joined the British Columbia Lions. In Calgary for a second time around, he did not enjoy the same success, throwing more interceptions than touchdowns in 1973 and 1974. In 1975, his last season, still with the Lions, he completed 152 of 280 passes for 2310 yards and 13 touchdowns with 9 picks.
Liske left the private sector in 1985 for the University of Washington in Seattle, where he started as an associate athletic director, with a focus on fundraising and promotions. He became the athletic director at the University of Idaho in Moscow in 1992, and moved to the University of Toledo in 1996. In late 2001, Liske returned to his alma mater, Penn State, where he was appointed director of major gifts for intercollegiate athletics, with special emphasis on developing funding for the improvement of athletic facilities.