Hailing from Wagga Wagga, Suckling played football with Isaac Smith in the Wagga Hawks for several years before both moved to the Wagga Tigers where they won two premierships.
Rookie
First drafted by the Hawthorn Football Club at pick 22 in the 2007 Rookie Draft. He was struck down by osteitis pubis for most of 2007 but was retained on the rookie list for 2008. Suckling was redrafted to Hawthorn's rookie list by the club at pick 81 in the 2009 Rookie Draft. At the 2009 rookie draft, where Hawthorn had agreed to redraft Suckling; the club mistakenly read out the wrong player registration number and accidentally selected the Sandringham Dragons' best-and-fairest player, Matthew Suckling He was then finally drafted to Hawthorn's senior list with pick 70 in the 2009 AFL Draft.
Career
He made his debut for Hawthorn in the opening round of the 2009 AFL season in the rematch of the 2008 AFL Grand Final against Geelong. The 20-year-old defender was one of three Hawks playing their first game in the MCG blockbuster. Omitted the next week because of injury, Suckling was unable to break back into the side; he was listed as an emergency later in the year. In 2010 he played five games, and was on the verge of selection for most of the season. 2011 was a breakthrough year for Suckling; with his precision kicking and link-up play he became a key to Hawthorn's defence. Characteristic of his style of play is his very long range, very accurate kicking. Suckling was selected as the Australia international rules football team's goalkeeper for the 2011 International Rules Series in Australia. Australia lost the series 2–0, with a 130–65 aggregate score. Suckling was one of two Hawthorn players selected for the team, along with Liam Shiels. Suckling was one of three Hawthorn players to play every game in 2012. During the 2013 NAB Cup pre season competition Suckling tore his anterior cruciate ligament whilst playing against Richmond. Suckling missed the entire 2013 season due to the injury that required a full knee reconstruction. Suckling returned to the side in 2014, and would go on to claim his elusive premiership medal in the club's 2014 Grand Final win. He followed this up with a premiership win in 2015, starting the game as a substitute and coming on late in the third quarter for David Hale; with the abolition of the substitute rule at the end of the 2015 AFL season, this meant that Suckling became the last player to be substituted into a game. Following the Grand Final, Suckling exercised his right as a free agent and joined the Western Bulldogs. In his first season at the Western Bulldogs Suckling was unfortunate to miss the Preliminary Final and Grand Final victories with an Achilles injury