Groat joined the Wests Tigers NYC Cup team in 2011. By round 12 he had progressed to making his début in first grade, after a late injury to Wade McKinnon. Having already played a lower-grade game, Groat came off the bench in the last 5 minutes.[16] Later in the season, Groat became a regular in the first side, playing off the bench. Wests Tigers won 8 of the 10 games he played in 2011.
In an early-season match in 2012, Groat was knocked unconscious by a shoulder charge from Brisbane Broncos forward Ben Te'o.[17] The incident was considered a "test case" on how the NRL Judiciary would treat players who made contact with the head when attempting a shoulder-charge.[18] Two weeks later Groat played for New South Wales in the inaugural under-20s State of Origin match,[19] but he failed to make a further first grade appearance for the season.
Groat was unable to play at the start of 2013 due to injury. Coach Mick Potter said, "Matt got his ankle, foot and toe caught in the ground and got some weight on the back of it. He had been working hard and his shape was looking better too."[20] He didn't play any first grade in 2013.
St. George Illawarra Dragons
In September 2013, it was announced that Groat had signed with the Dragons for at least one season.[21] He failed to make any first-grade appearances for the club, and a year later signed with Salford.[22]
Doncaster
On 16 April 2015, Groat signed for English side Doncaster.[23] Total Rugby League reported that the 23-year-old prop arrived “with a high pedigree”, having played 17 NRL games for the Wests Tigers and spending the previous year with St George Illawarra.[24]
Dewsbury
On 29 January 2016, Groat was released by Doncaster and signed with Dewsbury.[25] He featured regularly in the front row, making 24 league appearances and scoring one try.[10]
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