Schremp grew up in Fulton, New York. As a youth, he played in the 1999 and 2000 Quebec International Pee-Wee Hockey Tournaments with a minor ice hockey team from Rochester, New York. He decided a move to Canada would benefit his hockey career and he spent his major junior years in the Ontario Hockey League. He spent his rookie season with the Mississauga IceDogs and after recording 26 goals and 74 points in 65 games, was named OHL rookie of the year for 2002–03. Just three games into the 2003–04 season, Schremp was traded to the London Knights, the team with which he would spend the final three seasons of his OHL career. He began to impress during the 2004–05 season, scoring 41 goals and 90 points in 61 games as well as 13 goals and 29 points in 18 playoff games as he helped London win their first Memorial Cup. That season, Schremp was also selected to play for the United States at the 2005 World Junior Championships, where he scored four goals and five points in seven games as the Americans finished in fourth place. The 2005–06 season capped off a prolific junior career for Schremp, as he led the OHL in scoring with 57 goals and 145 points in only 57 games before adding ten goals and 47 points in 19 playoff games. Schremp once again represented the U.S. at the 2006 World Junior Championships, recording six points en route to a second consecutive fourth-place finish.
Professional
NHL
Drafted by the Edmonton Oilers in the first round of the 2004 NHL Entry Draft, Schremp made his professional debut during the 2006–07 season with the Wilkes-Barre/Scranton Penguins, the Oilers' then-American Hockey League affiliate. He also made his NHL debut that season, dressing for the Oilers in a game against the Minnesota Wild on April 5, 2007. Schremp, however, had difficulty securing a permanent roster spot with the Oilers and found himself playing primarily for the AHL's Springfield Falcons—the team's new AHL affiliate—over the following two seasons, seeing only limited action with Edmonton. He accumulated 171 points in 216 AHL games during that period, as well as three points in seven games with the Oilers. On September 29, 2009, Schremp was claimed off waivers by the New York Islanders. He found more regular time with the Islanders, playing 44 games during the 2009–10 season. His first NHL goal came on December 12, 2009, in a game against the Boston Bruins. That season, Schremp tallied seven goals and 25 points. Schremp posted another ten goals and 22 points in 45 games with the Islanders during the 2010–11 season, but on February 28, 2011, was claimed off waivers by the Atlanta Thrashers. He then scored his first goal as a Thrasher on March 9 against the Carolina Hurricanes, and finished the season with three goals and four points in 18 games with Atlanta for a total of 26 points in 63 games. When the Thrashers were purchased and relocated to Winnipeg to become the Jets in May 2011, Schremp was not tendered a qualifying offer and thus became an unrestricted free agent.
Europe
On August 10, 2011, Schremp signed with Modo Hockey of the Elitserien in Sweden. He enjoyed a successful debut season in Sweden amongst the top scoring line in Modo, contributing 19 goals and 41 points in 55 games. On June 1, 2012, Schremp opted to sign a lucrative two-year contract with Dinamo Riga of the Kontinental Hockey League. During the 2012–13 season, however, he failed to transition to the KHL, scoring only one goal in 21 games before leaving the team in November 2012 to sign a contract with Red Bull Salzburg of the Austrian Hockey League through the remainder of the season. After re-establishing his offensive game with Salzburg, Schremp impressed SwissNational League A club EV Zug and subsequently signed a one-year contract for the 2013–14 season on May 17, 2013. He scored 36 points in 42 games as Zug failed to make the playoffs though nonetheless avoiding relegation. On July 8, 2014, Schremp continued his journeyman career, agreeing to play for his seventh European club in only his fourth season abroad, after signing a one-year contract with Metallurg Novokuznetsk of the KHL. Just two months later, In September 2014, it was announced that he left Metallurg to join Skellefteå AIK in the Swedish Hockey League. He advanced to the 2014–15 SHL Finals with Skellefteå, where they fell short to the Växjö Lakers. On September 9, 2015, Schremp returned to North America after four years in accepting a try-out contract with the Portland Pirates of the American Hockey League, an affiliate of the Florida Panthers. He led the Pirates in scoring during the 2015–16 season, talling 21 goals and 21 assists in 75 regular season contests and also played in five postseason games. On May 24, 2016, the SCL Tigers of the Swiss top-flight National League A announced the signing of Schremp on a one-year deal. Schremp parted ways with the SCL Tigers on January 31, 2017. He had tallied ten goals and 17 assists in 33 NLA appearances for the club. He was picked up by the Nürnberg Ice Tigers of the German DEL the next day. In November 2018, Schremp announced his retirement.
