2006-07: Connolly was selected by the Prince George Cougars in the first round (10the overall) of the 2007 WHL Bantam Draft.
2007-08: Connolly made his WHL debut and was scoreless and -3 in four games with Prince George. He scored 16 goals with 16 assists and 80 PIM in 38 games with the Cariboo Cougars in the BCMML. In six BCMML playoff games, he scored 4 goals with 1 assist and 10 PIM.
2008-09: Connolly scored 30 goals with 30 assists with 38 PIM in 65 games as a rookie for Prince George. Twelve of his 30 goals were scored on the power play which partly explains his -26 PIM with the fourth-place Cougars. He had 2 assists with 6 PIM and was -2 in four playoff games as the sub-.500 Cougars were swept by BC Division regular season champ Vancouver in the first round of the playoffs. Connolly represented Canada Pacific at the World U-17 Hockey Challenge and scored 3 goals with 5 assists in six games. He scored 3 goals and added 3 assists with 4 PIM in 6 games for Team Canada at the WJC U-18 tournament. Connolly was named the WHL and CHL Rookie of the Year.
2009-10: Connolly suffered a hip injury at the 2009 Ivan Hlinka Memorial Tournament prior to the WHL season and missed much of the season. He played in 16 games for the Cougars and scored 10 goals with 9 assists and was -3 with 8 PIM. Connolly scored three times on the power play and had two short-handed goals. He was named to the 2010 CHL Top Prospects Game but had to withdraw due to his injury. Connolly was chosen in the first round, 6th overall, of the 2010 NHL Draft by the Tampa Bay Lightning.
2010-11: Connolly was the leading scorer for the WHL’s Prince George Cougars despite missing nine games due to a sprained knee. Connolly appeared in just one playoff game for the Cougars after separating his shoulder. In 59 regular season games he scored 46 goals with 27 assists and was -5 with 26 PMs. Fifteen of Connolly’s goals were scored on the power play. Connolly skated for silver medal-winning Canada at the 2011 U20 World Junior Championship and was +2 with 3 assists in seven games.
Connolly is a pure offensive talent who can make plays at a high rate of speed. He can score goals as well as set them up. Connolly will have to adjust to the tighter checking, physical nature at the level of the pro game but he is an elite talent capable of dominating games. Connolly's hip injury was a big source of concern heading into the 2010 draft but a preliminary report indicated that he is recovering and was impressive during the summer prospect camp with the Lightning. He has added size to his frame since his early junior days and is much stronger on the puck in tight areas.
Connolly was deal by the Tampa Bay Lightning to the Boston Bruins in exchange for two second round picks.