[12] Scouts described Connolly as a natural leader with good on-ice awareness who plays in the style of a power forward.

[13] Attending his first NHL training camp in September 2010, Connolly was returned to the Cougars to continue developing at the major junior level for the 2010–11 season.

Whilst playing in his fourth WHL season, he was named captain of the Cougars and recorded 73 points over 59 games, leading his team in scoring.

[15] His first professional season, however, was interrupted when he was loaned to Team Canada for a second-straight appearance at the IIHF World U20 Championships.

On September 14, 2012, the Tampa Bay Lightning assigned Connolly, as well as 17 others, to the American Hockey League (AHL)'s Syracuse Crunch during the 2012–13 NHL lockout.

[20] Connolly would then remain with Syracuse, where he helped the Crunch reach the Calder Cup Final against the Grand Rapids Griffins, though the team would be defeated in the six-game series.

[21] In preparation for the upcoming 2013–14 season, Connolly had a strong training camp with the Lightning, scoring four goals during the pre-season.

Explaining the demotion, Lightning General Manager Steve Yzerman stated, "I don't want Brett playing on the fourth line.

[28] On October 24, Connolly played in the first period against the Winnipeg Jets, but he would miss the rest of the game with a lower body injury.

[31] On December 6, Connolly played in his 100th career NHL game in 3–1 Lightning loss to the Columbus Blue Jackets.

On April 3, Connolly made his debut with the Bruins, recording two assists in Boston's 3–2 win over the Detroit Red Wings.

[35] Unable to live up to his draft expectations with the Lightning and the Bruins, Connolly as a restricted free agent was not tendered a contract by Boston.

On July 1, 2019, having left the Capitals as a free agent after three seasons, Connolly was signed to a four-year, $14 million contract by the Florida Panthers.

In the following pandemic delayed 2020–21 season, Connolly struggled to repeat his offensive totals, producing just 2 goals and 4 points through 21 games before he was placed on waivers by the Panthers and assigned to the taxi squad.

In the following 2021–22 season, after attending training camp, Connolly was placed on waivers and re-assigned to begin the year with AHL affiliate, the Rockford IceHogs.

On July 11, 2022, Connolly was placed on unconditional waivers by the Blackhawks for the purpose of buying out the remaining year on his contract, he was released as a free agent the following day.

[40] In leaving the NHL and North America after 11 seasons, Connolly embarked on a European career in agreeing to a one-year contract with Swiss club, HC Lugano of the NL, on September 5, 2022.

Connolly declined the traditional White House visit after the Capitals won the Stanley Cup, stating that "It has nothing to do with politics, it’s about what’s right and wrong.”[50] His wife Katrina is also from Canada.