[2] He played his junior rugby league for the All Saints Toongabbie Tigers, before being signed by the Canterbury-Bankstown Bulldogs.

[7] In 2012, Klemmer was named on the interchange bench for New South Wales in the inaugural under 20s State of Origin match at Penrith Stadium.

In round 4 against the Melbourne Storm, Klemmer scored his first NRL career try in the Canterbury club's 40–12 win at nib Stadium in Perth.

[18] On 5 October 2014, in Canterbury's 2014 NRL Grand Final against the South Sydney Rabbitohs, Klemmer played off the bench in the club's 6–30 loss.

[21][22] In round 5 of the 2015 NRL season, in the Grand Final re-match against the South Sydney Rabbitohs, Klemmer was sin binned after crowding in on referee Gerard Sutton alongside Canterbury captain James Graham and yelling "You're off your f***ing face".

[23] After full-time was blown, some members of the Canterbury fan base pelted referee Gerard Sutton and match officials with plastic bottles, causing an investigation to find out and ban the misbehaving members from attending rugby league matches for life.

[31][32] In game 2 of the 2015 State of Origin series, he again made headlines after a heated exchange with the oldest member of the Queensland team, Corey Parker.

[39][40] After Game 2, Klemmer got into some trouble after the Blues 26–16 loss to Queensland after he punched a wall in frustration in the toilets off the Suncorp Stadium changing rooms.

[46] In June 2017, it was rumoured that Klemmer requested a release from his contract from Canterbury-Bankstown due to a financial dispute stemming from his decision to split with long-time manager David Riolo.

On 3 October 2017, Klemmer was selected in the 24-man Australia Kangaroos 2017 Rugby League World Cup squad.

[54][55] In 2018, Klemmer was selected to play for New South Wales in the 2018 State of Origin series which The Blues emerged victorious winning 2–1.

It was alleged that Klemmer refused to be substituted towards the end of the match and verbally abused a Newcastle trainer.

[64] On 16 November, Klemmer joined the Wests Tigers on a three-year deal in a player swap with Jackson Hastings.

[68] In round 4 of the 2024 NRL season, Wests Tigers won 17-16 over Parramatta at the Western Sydney Stadium.

Klemmer was alleged by some fans online of cheating as he waved his arms and jumped in front of the goalposts as Gutherson moved to kick the ball, a distraction which is against the rules.