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Conrad joined Thistle at the start of the 2010/11 season, initially on loan from Hearts. After playing in a couple of pre-season fixtures, he then made his competitive debut as a substitute against Raith Rovers in the opening league game of the season.
After spending the whole of that season at Firhill, he joined up again on loan for the first half of the following season. Despite returning to Tynecastle for a short period, the defender was a Partick Thistle player again come the February signing a deal to keep him at the club until the end of the season before signing a two year deal during the summer of 2012.
Season 2012/13 was his first full season as a Partick Thistle player and he marked it by scoring six goals, helping the side to the First Division championship and taking a clean sweep of supporters’ Player of the Year awards, becoming a firm fans favourite in the process.
With promotion back to the top flight of Scottish Football secured, Conrad signed a two year contract extension keeping him at Firhill until the end of the 2014/15 season.
Conrad made the step up to Premiership standard well, partnering firstly Aaron Muirhead then Lee Mair as Thistle battled to Premiership survival in 2013/14, making 34 appearances scoring two goals. His only league goal of the season came in a game against Aberdeen in February 2014; a win which finally saw Thistle end a long home winless streak.
He continued to play well in the heart of the Thistle defence in 2014/15 forging strong partnerships with both Dan Seaborne and Frederic Frans.
Conrad was offered a new deal at the end of the 2014/15 but turned it down, instead opting to find a fresh challenge after five seasons at Firhill and over 150 appearances.