Lindsay was born in Glasgow and attended St Ninian's High School in Giffnock where he played in the schoolfootball team along with Andrew Robertson. After joining the youth system at Partick Thistle in 2011, Lindsay signed his first professional contract with the club on 6 June 2012. He made his debut for the club in their final match of the 2012–13 season, a 0–0 draw away to Dumbarton on 4 May 2013. On 31 January 2014, Lindsay signed for Scottish Championship club Alloa Athletic on loan for the rest of the 2013–14 season. He made his debut on 1 February 2014, as Alloa drew 1–1 with Dundee. He played 11 times for Alloa helping them to avoid a relegation play-off. After returning to Partick Thistle, Lindsay signed a new two-year contract with the club in June 2014. Lindsay made his full Scottish Premiership debut, playing 90 minutes on 4 January 2015, in a 2–2 draw with high-flying Dundee United. On 29 January 2015, Lindsay signed for Scottish League One side Airdrieonians on a loan deal until the end of the 2014–15 season. Lindsay played 13 matches for Airdrieonians scoring once in a 1–0 away win against Peterhead on 25 April 2015. Lindsay broke into Thistle's first team in the 2015–16 season after impressing manager Alan Archibald in pre-season. He scored his first goal for Partick Thistle in a 1–1 draw with Dundee on 8 December 2015. He was sent-off twice during the campaign firstly against Kilmarnock in August 2015 and then against Dundee in January 2016. Lindsay played 27 times in 2015–16 as Thistle finished in 9th position. He became a main stay of the defence in 2016–17 which saw him make 42 appearances, scoring seven goals as the Jags finished in 6th position after. Lindsay was named in the Scottish Premiership 2016–17 Team of the Year; he was only player outside of Aberdeen and Celtic to be in the team.
Barnsley
In June 2017 he turned down a prospective transfer to English club Oxford United. Later that month Partick Thistle accepted an offer for Lindsay from Barnsley. Lindsay signed a three-year contract with Barnsley on 22 June. He made his Barnsley debut on 26 August 2017 in a 3–0 victory against Sunderland. Lindsay settled into life at Barnsley well and by November 2017 there were calls for him to earn a Scotland call-up. However Barnsley hit poor form around December and they ended up being relegated after losing 4–1 at Derby County in the final match of the 2017–18 season. In 2018–19 under the management of Daniel Stendel, Lindsay formed a strong partnership with Ethan Pinnock as the Tykes held the best defensive record in the EFL with only 39 goals conceded and kept 21 clean sheets helping them secure second spot and a return to the Championship at the first time of asking.
Stoke City
Lindsay joined Stoke City on 25 June 2019 for an initial fee of £2 million, rising to £2.5 million, along with Barnsley teammate Adam Davies. Lindsay made his debut on 10 August 2019 in a 3–1 defeat against Charlton Athletic. He scored his first goal for Stoke against Birmingham City on 31 August 2019. The team began the season in poor form and were struggling at the bottom of the table which resulted in a change of manager in November 2019. Lindsay kept his spot in the team until Michael O'Neill brought in James Chester in January and he took Lindsay's place for the remainder of the 2019–20 season.
Personal life
Lindsay's uncle Ricky Gillies is also a professional footballer, whilst his father, James, was once on the books at Celtic.
