Born in Liverpool, Merseyside, Coady grew up supporting Liverpool. He is a product of the Liverpool Youth Academy after joining the club in 2005. During the 2010–11 season, Coady was on the fringes of the first team, making the subs bench twice but failed to make a first-team appearance. Coady played every Reserve League and NextGen Series match during the 2011–12 season, scoring five goals. Despite being named in the senior squad list and being called up to the senior squad occasionally from 2009, he did not make his senior début until 8 November 2012 in a UEFA Europa League group stage match against Anzhi Makhachkala. After Andre Wisdom's promotion as a full-time senior squad member, Conor Coady was installed as full-time captain of the Under-21 squad and on 12 May 2013 he made his Premier League debut in a 3–1 win at Fulham. Coady agreed a six-month loan deal with League One club Sheffield United on 22 July 2013, later stating that he had turned down the chance to go on Liverpool's pre-season tour of Australia and the Far East in order to join up with his new club. Coady made his debut for the Blades in the opening fixture of the following season, coming on as a second-half substitute in a 2–1 home victory over Notts County, and made his first start for the club in the following game, a League Cup first round defeat to League Two club Burton Albion. Coady scored his first senior goal in a 1–1 draw at Leyton Orient on 30 November 2013. Having been in and out of the team during the first half of the season, Coady began to cement a regular first-team place over the Christmas period, prompting United to extend his loan spell during the January transfer window, and once more in February to extend his stay until the end of the season. Coady played regularly for the Blades for the remainder of the season and returned to Anfield having played 50 games and scored six goals.
Huddersfield Town
On 6 August 2014, Coady signed for Championship club Huddersfield Town on a three-year deal for a fee believed to be around £500,000. He made his debut as a substitute in the 4–0 defeat by Bournemouth on 9 August. On 1 October, he scored his first goal for the club against Wolverhampton Wanderers where Town won 3–1 at Molineux Stadium. He again found the net, this time in a 2–2 draw against Rotherham United.
Wolverhampton Wanderers
On 3 July 2015, Coady signed for Championship club Wolverhampton Wanderers on a three-year deal for an undisclosed fee, believed to be around £2 million. He scored his first goal for Wolves in a 2–1 EFL Cup first round win against Crawley Town on 9 August 2016. As of the start of the 2017–18 season under manager Nuno Espírito Santo, Coady played in the centre of a three-man defence for Wolves. In September 2017 that year he signed a new four-year contract. On 21 April 2018, during his 120th league appearance for Wolves, Coady scored a 66th-minute penalty in a 4–0 win against Bolton Wanderers to get his first league goal for the club, as Wolves sealed the EFL Championship title. On 15 February 2019 Coady signed a new contact lasting to the summer of 2023.