He attended Mount Scopus Memorial College, of which he graduated in 1998. As a young batsman, Klinger was named Captain of the Australia Under 19's Mens Cricket team – his deputy being Michael Clarke latterly Australia Vice Captain and as of 2011 Captain of the Test and ODI teams.
Klinger began as an 18-year old youngster in the 1998–99 season. His career lowlight was the 2000–01 season when he made a famous 99 not out, with captain Paul Reiffel declaring the innings closed, a move which brought great controversy and remains the only batsman in Australian cricket to be stranded on 99 due to a declaration. This caused Klinger some great upset, and following it Klinger had several less successful years, but returned to contention for a spot in the Victorian Bushrangers side for the 2005–06 season. He quickly made his first first-class cricket century, and then followed it up with his first List A one-day century, but his first class form soon dropped, and he was replaced in the side by Lloyd Mash, not to return in the Pura Cup all season. In 2003 he was the club professional for Walkden in the Bolton Cricket League.
In Season 2006–07 he started off in the outer from the Pura Cup side, but started off his Ford Ranger Cup season in style, nearly getting a century early on, and then following it up with one. He led the runs scoring in the competition for much of the season, eventually finishing 3rd. Klinger's rise to the Pura Cup team came only when Brad Hodge was called up by Australia for their ODI Series, and Klinger's recent form had been wavy, with his last game for the 2nd XI yielding a first innings duck, but second innings century. Klinger was soon to do the same for the 1st XI, but the century ensured that when Hodge returned, Klinger survived. He finished the season as a regular fixture of the Bushrangers side, and was part of a great partnership with David Hussey in a match against NSW, in which the Vics defied all odds to chase down a massive total of 360 on an extremely poor 4th day pitch (it was later described as a 3rd day pitch on day 1 by Hussey), scoring 102.
Klinger joined the South Australia Redbacks for the 2008–09 season in order to get more opportunities at state level, where he began batting at number 3 rather than opening, and saw immediate success, scoring a maiden 150 against old state Victoria in his first game. Then, against Western Australia on 11 November, Klinger scored his maiden double century, finishing on 255, and he continued to score heavily in both the Sheffield Shield and the Ford Ranger Cup, and hit his third century for the season against Queensland at the Gabba, and his first away from the traditionally batting friendly Adelaide Oval.
On 11 December 2008, Klinger posted his highest individual score in one day cricket, with an unbeaten 133 off just 128 balls. This guided South Australia to victory in their high-scoring match against the Tasmania Tigers at the Adelaide Oval. This was Klinger's fourth one-day century. He won the Australian Cricketers' Association's December 2008 Johnnie Walker player-of-the-month award.
In 2010, Klinger was named Captain of the Redbacks.
In December 2012, Klinger was signed by English county Gloucestershire, not only as their overseas player for the 2013 season, but also as their captain, taking over from Alex Gidman. He had previously stood in for Phil Hughes at Worcestershire at the beginning of the previous season. He scored over 1000 runs in the County Championship, scoring 6 centuries, plus another 1000 runs in the limited over competitions. Due to his success, Klinger returned to captain Gloucs again for the 2014 season. He was their leading run scorer in the One Day Cup, until he broke his arm playing against Derbyshire in August.