Originating from Bogutovac, Glavčić was born in Kraljevo. He started training for football at the age of 5 with local football school "Bambi".[1][2] He played for youth categories of Sloga Kraljevo until 2011, when he joined Partizan.[3] He was loaned to Teleoptik for the 2014–15 season.[4] Glavčić signed his first professional five-year contract with Partizan on 18 June 2015.[5] He made his Serbian SuperLiga debut in 3rd fixture of 2015–16 Serbian SuperLiga, against Novi Pazar.[6] During the winter break off-season, Glavčić returned to Teleoptik, where he spent the rest of 2015–16 season.[7] In summer 2016, Glavčić terminated the contract with club.[8]
Spartak Subotica
Glavčić moved to Spartak Subotica in summer 2016 and signed a three-year professional contract with the club.[9] He started the 2016–17 Serbian SuperLiga season as the back-up option, having split playing time with Nnaemeka Ajuru for the first half-season. During the second half-season, Glavčić played mostly matches, pairing with Marko Pantić on two defensive midfield positions. During the season, Glavčić made 33 matches in both domestic competitions at total, under coach Andrey Chernyshov.[10] Glavčić scored his first goal for Spartak Subotica in 3–2 victory over Mačva Šabac on 14 August 2017.[11] He also scored in the Serbian Cup match against Polet Lipljan on 20 September same year.[12]
Slaven Belupo
On 9 July 2019, Glavčić signed for Prva HNL club Slaven Belupo.[13] He scored his first goal on 30 October 2019 in a Croatian Cup match against BSK Bijelo Brdo, which Slaven won 2–0.[14] Upon arrival of new coach Tomislav Stipić, Glavčić soon turned into one of the key parts of the Slaven squad.[15] He scored his first Prva HNL goal on 22 August 2020 in a 2–1 defeat to Gorica.[16] On 16 October, he scored once and assisted Tomislav Božić twice in a 5–1 routing of Istra 1961. He also notably assisted Stipe Bačelić-Grgić in a 2–2 draw with Hajduk Split and Törles Knöll in a 3–3 draw with Dinamo Zagreb on 29 August and 19 September, respectively.[17] His great performances in Croatia sparked debates in Serbia about whether Partizan gave up on the player too early.[18]
Khimki
On 18 January 2022, he signed a 2.5-year contract with Russian club Khimki.[19]
Volos
On 27 June 2023, he joined Volos on a free transfer. [20]
International career
Glavčić has been called up to the Serbia national team selections since 2012. As a youth player, he represented the country passing all selections from under-16 to under-19 level. In November 2016, he was also called into the Serbia national under-20 football team under coach Nenad Lalatović for a friendly match against Montenegro, after which he appeared as a regular team member until 2017.[21]