Pantić made his debut on 26 May 2013 in a league fixture against Spartak Subotica, replacing Vladimir Volkov in the 70th minute. After a disagreement with Partizan over contract extension proposals, he signed a one-and-a-half year contract with Partizan on December 5, 2013. Juventus had scouted Pantić since early 2014, allegedly monitoring his status due to his short contract. After hearing about interest from Juventus, Pantić told Večernje novosti that he wished to extend his contract with Partizan before leaving Serbia.
Chelsea
On 13 July 2015 Pantić signed for Chelsea for a reported fee of £1.25 million, on a four-year deal and was immediately loaned out to Eredivisie side Vitesse Arnhem.
Loan to Vitesse
He made his Vitesse debut 17 days later in a UEFA Europa League third qualifying round first leg against Southampton at St. Mary's, replacing Valeri Kazaishvili for the final 23 minutes of a 3–0 defeat. On 9 August 2015, Pantić made his league debut in a 1–1 draw with Willem II, replacing Valeri Qazaishvili in the 71st minute. On 3 March 2016, after being supposedly 'frozen' out of the Vitesse starting eleven, Pantić stated his passion for a return to London: "I want to come back to Chelsea, just to train. Why am I in Vitesse if I am not good enough? I am crazy! I've made no mistake. If I had a chance and blew it, I would keep quiet. Maybe in Vitesse they don't like us Serbs: Nemanja Matić did not get a chance here either and Uroš Đurđević played 22 matches in a year and a half." Following this interview, Pantić was suspended by first-team manager Rob Maas indefinitely.
Loan to Excelsior
On 12 August 2016, Pantić joined Excelsior on loan for the 2016–17 campaign. On 17 September 2016, Pantić made his debut against Willem II off the bench coming on after half-time as Excelsior went on to score a late goal to earn a 1–1 draw. In the following match, on 20 September, he made his full debut, playing a full 90 minutes in a 1–0 win over BVV Barendrecht in the KNVB Cup.
Loan to Partizan
On 18 June 2017, Pantić returned to his boyhood club, Partizan on a season-long loan. On 22 July 2017, Pantić scored a goal against Mačva Šabac in first fixture of the 2017–18 Serbian SuperLiga season in a 6–1 home league win. On 5 November, Pantić entered in a game as a substitute for Marko Janković in the 72nd minute and with two assists help club to reach a 3–1 away victory over Mačva. That match is a big turn for Pantić, because after that match he played in first eleven almost every match until the end of the season. On 23 November 2017, he start in a five match of 2017–18 UEFA Europa League group stage, against Young Boys, he made one assist and was one of the best Partizan players on that match, where Partizan advanced to the knockout stage after 13 years. In second part of the season, Pantić scored a couple a very nice goals and had a couple assist. Due to his consistent performances throughout the season, Pantić was named in the league's best eleven. On 5 July 2018, Pantić's loan at his boyhood club was extended for a further season.