Klonaridis emerged from the AEK Athens FC academy as a young prodigy, signing his first professional contract with the club at the age of 18. During his first stint at the club, he made some notable appearances against Panathinaikos FC where he scored his first professional goal in the GreekSuperleague and then proceeded to score 3 more goals in the championship. After his impressive performances in the championship and in European football, he secured a transfer with Lille OSC.
Lille
On 2 July 2012, Klonaridis signed a three-year contract with Lille OSC for a reported fee of €800,000. On 31 January 2013, he joined Belgian Second Division side Mouscron-Péruwelz on loan from Lille.
Panathinaikos
On 2 September 2013, Klonaridis joined Panathinaikos as a free agent on a four-year deal. On 25 September 2013, he scored on his debut, against Ergotelis in the Greek Cup. On 10 November 2013, he netted twice in a 2–0 win against Aris. On 14 May2014, he helped his club claim Greece's second Champions League spot scoring in a 1–1 draw against Atromitos in the playoffs, which left Panathinaikos with an unassailable lead at the top of the table with one match left. At the beginning of 2015–16 season, Klonaridis faced injury problems causing him to train separately from the rest of the squad. On 28 October 2015, he scored his first goal for the season, playing in the Greek Cup against Levadiakos. On 3 December 2015, Panathinaikos won 2–1 against Panachaiki at Pampeloponnisiako Stadium thanks to a brace scored by him in the first half. On 23 May 2016, he scored in a 3–0 defeat of rivals AEK Athens reaching 100 appearances with for Panathinaikos. On 14 August 2016, Panathinaikos accepted a bid from Belgian club Lokeren for a transfer fee, reported to be in the region of €300,000. However, the move was not completed.
On 31 August 2016, the last day of the summer window transfer, Klonaridis returned to France, signing a two-year contract with Ligue 2 club Lens, for an undisclosed fee.
Loan to Panathinaikos
On 30 January 2017, Klonaridis returned to Panathinaikos, initially on loan, but with an option for the Greek club to sign him permanently. On 31 May 2017, his goal and overall positive performance, helped his club to succeed an away 3–2 win against rivals PAOK in the last matchday of the 2016–17 Playoffs depriving them of the possibility to participate in the UEFA Champions League third qualifying round.
Return to AEK Athens
On 29 June 2017, Klonaridis joined Super League side AEK Athens by signing a contract until June 2020. AEK paid €200,000 to acquire Klonaridis from Lens. On 8 August 2018, he scored before the break in a 1–1 away draw for UEFA Champions League Third qualifying round, 1st leg against Celtic. On 22 August 2018, he scored, slamming home the rebound from close range after Anastasios Bakasetas' snapshot had been parried by MOL Vidi's goalkeeper Ádám Kovácsik in a glorious 2–1 away win for UEFA Champions League Playoffs, 1st leg against MOL Vidi. On 16 September 2018, Klonaridis scored his first brace with the club in a 4–0 home win game against Panionios, as six minutes from full time with a brilliant piece of individual skill, skipping past the challenge of Luis Gustavo Dominques before firing a powerful shot beyond Panthers goalkeeper Filip Manojlović and at the last minute of the match scoring his second of the night, slotting home after good work from striker Marko Livaja. On 2 October 2018, he scored a brace in a 2–3 loss UEFA Champions League home game against Benfica. In both goals, he scored with a right footed shot from very close range after assisted by Niklas Hult and Marios Oikonomou respectively, but after the AEK forward missed a great chance for his hat-trick, Alfa Semedo’s long-range strike won it for Benfica on the counter attack. He has become the team’s first player in history to score twice in one single group match. On 22 January 2020, Klonaridis scored his first goal for the season, after a Hélder Lopes assist, in a 3–1 away win against Volos. The speedy 27-year-old has previously been plagued by injuries this season. The goal was Klonaridis’ first since 2 October 2018, when he scored twice in a 3–2 home defeat to Benfica in the UEFA Champions League group stage. On 1 March 2020, Klonaridis scored a stunning goal in stoppage time to salvage a thrilling 1–1 away draw for AEK against Panionios. On 30 June 2020, Klonaridis solved his contract with the club. At times, the talented 27-year-old forward showed glimpses of his potential, but he was often hindered by injury problems and a lack of consistency.
APOEL
On July 7, 2020 he joined Cypriot club APOEL on a free
