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 (AHL) 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.