Born in Glasgow and raised in Eaglesham in East Renfrewshire, Wallace began his career as a trainee at home town club Rangers before joining the academy at Falkirk aged 16. He made his first team debut on 6 August 2011 as a substitute in Falkirk's 1–0 defeat to Raith Rovers in the Scottish First Division. He went on to make his first league start on 13 August 2011 against Partick Thistle at the Falkirk Stadium. He scored his first goal for the club on 5 November 2011 in a 4–3 win over Livingston. On 31 January, the last day of the January 2012 transfer window, Wallace signed for Huddersfield Town on a two-year deal, after rejecting moves to Brighton & Hove Albion and Ipswich Town. As part of the deal he was immediately loaned back to Falkirk for the remainder of the season, beginning with a start in the goalless 0–0 draw away at Greenock Morton on 11 February 2012. He went on to make 15 more appearances for Falkirk during the loan spell, making it a total 34 appearances for the club before returning to parent club Huddersfield, with his final appearance coming in a 3–2 win over Ayr as the Bairns finished the season in third position. He was also in the side as they won the 2011–12 Scottish Challenge Cup in April 2012, beating Hamilton Academical 1–0 in the final at Almondvale Stadium on 1 April 2012.
Huddersfield Town
Wallace returned to Huddersfield in May 2012 at the end of his loan at former club Falkirk. He was set to train with Simon Grayson's squad throughout the Play-Off campaign until he joined up with the Scotland Under-20 side ahead of a tournament being held in the Netherlands, as Huddersfield went on to win the Play-Off final beating Sheffield United on penalties to win promotion to the Championship. Wallace was given the number 15 shirt on 12 July 2012 when the squad returned to training for the 2012–13 season. He featured regularly for Huddersfield during pre-season receiving his first call up to the Scotland U21s in August 2012. After patiently waiting for his chance, Wallace made his Terriers debut as a substitute in the 1–1 draw against Blackpool at the John Smith's Stadium on 26 December 2012, and made his full debut three days later in their 0–0 draw with Sheffield Wednesday. His first goal for the club came in a 2–2 draw against Peterborough United on 6 April 2013. Wallace capped the season off by winning Young Player of the Year. In the following two seasons, he would make sporadic appearances for the Terriers, mainly due to only being selected when other centre-backs were injured or suspended.
Scunthorpe loan
On 25 August 2015, with appearances still being limited, Wallace joined Scunthorpe United on loan for a month in an emergency loan deal. After making 12 league appearances, he was recalled by Huddersfield on 1 November, along with team-mate Joe Lolley.
Scunthorpe United
Wallace signed a three-and-a-half year deal with Scunthorpe on 2 January 2016. Upon signing for the Iron, he featured in every minute of every competitive fixture until 29 August 2017, when his run of 7,560 consecutive playing minutes was broken as he didn't feature in Scunthorpe's Checkatrade Trophy game against Sunderland U21s.
Millwall
In June 2018, Wallace signed a "long-term" deal at Championship side Millwall for an undisclosed fee. He scored the winning goal in two consecutive rounds of the 2018–19 FA Cup as the Lions defeated Everton and AFC Wimbledon to reach the quarter-finals, but also collected two yellow cards and was suspended for the resulting match against Brighton which ended in defeat for Millwall on penalties.
International career
Wallace gained his first international call-up for the Scotland U20 side in May 2012 when he was named by head coachRicky Sbragia in the squad to compete in the 59th ADO Den Haag tournament. He made his debut in a 0–0 draw with Manchester City on 25 May 2012. and went on to feature in all five of Scotland's matches, playing the full 90 minutes in each, including the 1–0 victory over the hosts ADO Den Haag on 26 May, sending them through to the semi-final where the Scots lost 2–1 to Mexico, and then 1–0 to Cruzeiro in the third place play-off match. On 1 August 2012, Wallace received his first call-up to the Scotland under-21 team, after being named in the squad for their friendly match against Belgium on 14 August at East End Park, Dunfermline. He made his debut in the match on 14 August, playing the full 90 minutes in a 1–0 defeat.
