Markey played his youth football with Cherry Orchard, winning the Under 17FAIUmbro Cup with a 5–2 win over Leeds AFC in the final at Turners Cross on 3 May 2014. At the Ballyfermot club Markey played alongside future League of Ireland players Max Kouogun, Josh Collins and Derek Daly among others. Markey's form for the Orchard attracted interest from St Patrick's Athletic, who signed him for their under 19's side ahead of the 2014–15 season. This turned out to be a terrific season for both Markey as he won the league's Player of the Season award and also for the team as they won the Under 19 SSE Airtricity League with a 3–2 win over Derry City under 19's in the final at Maginn Park. The team included several players that broke through to the St. Pat's first team and beyond in the League of Ireland and English Football Leagues, including Jamie McGrath, Rory Feely, Jack Bayly, Fuad Sule and Paul Rooney.
Ahead of the St Patrick's Athletic senior team's 2015 season, Markey was called up to the first team for the season, given the number 21 shirt, he would also remain with the under 19's while still eligible. He made his first team debut on 9 February 2015, aged just 17 years old, when he came off the bench in a 7–0 win at home to Tolka Rovers in the Leinster Senior Cup. Markey made late substitute appearances in the President's Cup away to Dundalk and the first game of the 2015 League of Ireland Premier Division season away to Shamrock Rovers, his first Dublin Derby. Markey went on to make a further 5 appearances in the first team that season.
2016 season
In January 2016, Markey went on trial with Scottish Premier League champions Celtic, scoring in a trial game vs Kilmarnock. Nothing came of the move as Markey decided to take up the scholarship offer between St Pat's and NUI Maynooth, taking up a degree in finance at the college. To secure the degree, Markey would have to get the necessary points on his Leaving Cert, which he sat in June 2016. With the importance of his studies having to come before his football, the first half of 2016 turned out to be less productive for Markey as he made 7 league appearances and two league cup appearances that season as Pat's won the 2016 League Cup.
Markey changed squad number to the number 14 ahead of the 2017 season. On 17 April Markey made his first start for the first team in a win over Bray Wanderers in the League Cup. He then made his first league start 4 days later against Cork City at Richmond Park. His performances in these games stood out and earned him plaudits from fans, pundits and most importantly manager Liam Buckley, who kept him in the starting 11. He was nominated for the League of Ireland Premier Division Player of the Month for May 2017 but just lost out to Ryan Delaney. He went on to make a total of 18 league appearances, 22 in all competitions and his form in those games saw him voted as St Patrick's Athletic Young Player of the Year by the club's fans.
Markey's shirt number changed again to number 15 ahead of the 2018 season. He started the season out of the starting 11, having to come off the bench in the first few games but regained his spot in the Attacking midfielder role in the 0–0 draw with Dundalk. He scored his first senior goal on 15 May 2018 in a 5–2 win over Derry City at Richmond Park. His next goal came on 10 August when he opened the scoring in a 5–0 win over Inchicore Athletic in the FAI Cup First Round. The season proved to be a disappointment for his side as they missed out on European football once again, which saw the departure of Liam Buckley as manager. On a personal level for Markey however, the season was another big step in his development, making 36 appearances and scoring 2 goals.
Following on from a full season as a regular starter, Markey was given the number 8 shirt for the 2019 season. Markey had to wait until 15 March 2019 for his first appearance of the season under new manager Harry Kenny, coming on as a substitute in a 2–0 loss away to Waterford. He had to wait a month for his next appearance, making his first start of the season in a 1–1 draw away to Cork City. From then on he remained a mainstay in the team and on 17 May he scored his first goal of the season, opening the scoring in the Dublin derby against Bohemians with a looping header over James Talbot in the 40th minute. Markey saw his first taste of European football when he came off the bench away to IFK Norrköping of Sweden in a UEFA Europa League Qualifier, assisting Conor Clifford's goal in a 2–1 loss for Pat's. With the side struggling in front of goal, manager Harry Kenny was replaced by Stephen O'Donnell following a shock cup exit to UCD in late August and in O'Donnell's first match, Markey scored in a 2–1 win away to Finn Harps on 6 September 2019. He finished the season with 30 appearances and 2 goals in all competitions.
