2007-08: Daniel Carr played for the St. Albert Steel in the Alberta Junior Hockey League as a 16-year-old. He scored 16 goals with 11 assists and 36 penalty minutes in 62 games. The Steel finished seventh in the North Division and lost in a first round playoff series. Carr had no points nor penalties in five playoff games.
2008-09: Carr was the second-leading scorer for St. Albert in his second AJHL season. He scored 27 goals with 28 assists and 81 penalty minutes in 59 games. The Steel finished sixth in the North Division. In four playoff games Carr scored 2 goals with 2 assists and 2 penalty minutes.
2009-10: Carr joined the BCHL's Powell River Kings after Christmas after starting the year with St. Albert. He scored 10 goals with 17 assists and 14 penalty minutes in 22 regular season games with the Kings. Carr led the Kings with 15 goals and had 11 assists with 10 penalty minutes in 23 playoff games as Powell River reached the finals against Telus Cup-bound Vernon. Carr scored 24 goals with 30 assists and 15 penalty minutes in 30 AJHL games with St. Albert. He committed to playing college hockey at Union College in 2010-11.
2010-11: Carr led Union College with 20 goals as a freshman. Skating in 40 games for the Dutchmen he also had 15 assists and was +2 with 28 penalty minutes. Union finished first in ECAC Hockey in the regular season and received an at-large bid to the NCAA tournament after falling to Colgate in a three-game ECAC quarterfinal series. The Dutchmen lost to Minnesota-Duluth, 2-0, in a NCAA East regional semifinal game.
2011-12: Carr was Union College's third-leading scorer in his sophomore season. He scored 20 goals with 20 assists for 40 points, trailing only Jeremy Welsh (44) and Kelly Zajac (42). He skated in all 41 games for the Dutchmen and was +15 with 30 penalty minutes. Union finished first in ECAC Hockey and captured the league tournament title. The Dutchmen defeated Michigan State and Massachusetts-Lowell in the NCAA East regional tournament to reach the Frozen Four; falling to Ferris State, 3-1, in a semifinal game.
2012-13: Carr attended the Boston Bruins and Chicago Blackhawks prospect camps in the summer before returning to Union for his junior season. In 40 games he scored 16 goals, sharing the team lead with Wayne Simpson, and had 16 assists; finishing +3 with 26 penalty minutes. Union slipped to fourth in ECAC Hockey in the regular season but captured the league's playoff title to earn its third straight NCAA berth. The Dutchmen topped defending national champion Boston College, 5-1, in the East Regional semifinals before falling to ECAC rival Quinnipiac.
2013-14: Carr returned to Union College — becoming the program's all-time leading scorer at the Division I level — as the Dutchmen won their first national championship. Carr was Union's leading scorer with 22 goals and 28 assists (both career highs) and was +26 with 28 penalty minutes in 39 games. After losing back-to-back games in January the Dutchmen went 16-0-1 in their final 17 games, finishing first in ECAC Hockey and then winning the ECAC Hockey and Frozen Four tournament titles. The Canadiens signed Carr to a one-year entry-level contract on April 24th, 2014.
Montreal signed Carr to a two-year entry-level contract on April 24th, 2014.