|Date of birth||15 May 1991|
|Place of birth||Dubrovnik, SFR Yugoslavia|
|Height||1.94 m (6 ft 4 1⁄2 in)|
|2010–2011||→ Zadar (loan)||35||(1)|
|* Senior club appearances and goals counted for the domestic league only and correct as of 12 May 2016.
‡ National team caps and goals correct as of 5 September 2011
Glumac started his career playing at youth level for his hometown club GOŠK Dubrovnik. At the age of 15 he joined Hajduk Split where he eventually signed a professional five-year contract. In the second part of the 2009–10 season, he was loaned to Zadar to help the team avoid relegation. He was a first-team regular and played in 13 matches that season. He also remained at Zadar the following season and scored his first goal in Prva HNL in a 3–2 defeat to RNK Split. In the 2011–12 season, Glumac returned to Hajduk and made his debut for the first team on 21 October 2011 as a late substitute in the 3–0 win against Lučko. A month later, manager Krasimir Balakov announced that Glumac was no longer a part of the first team. On 9 January 2012, it was announced that Glumac was transferred to RNK Split in exchange for Goran Milović, signing a two-and-a-half-year contract.
Glumac was a part of the Croatian national under-19 team in the 2010 UEFA European Under-19 Football Championship held in France. Croatia reached semi-finals where they lost 2–1 to hosts but with this achievement they qualified for the 2011 FIFA U-20 World Cup. Glumac was selected in the 21-man squad by manager Ivica Grnja despite initial objection of Hajduk as they wanted to keep the defender in case of first-team injuries. Croatia finished in the last place in the group, losing all three matches to Saudi Arabia, Nigeria and Guatemala.
- Giant for Balıkesirspor
- Tomislav Glumac to set for Balıkesirspor on a loan deal
- Bajković, Drago (25 March 2010). "Nisam iznenađen dobrim rezultatima". Zadarski list (in Croatian). Retrieved 7 November 2011.
- Babić, Vedran (7 May 2011). "Split preko Zadra do Europe". Sportnet.hr (in Croatian). Retrieved 7 November 2011.
- Piršljin, Josip; Tolić, Josip (21 October 2011). "Lučko nedovoljno dobro za Hajduk". Sportnet.hr (in Croatian). Retrieved 7 November 2011.
- Zovko, Ante (21 November 2011). "Balakov otpisao mladi trojac". Sportnet.hr (in Croatian). Retrieved 21 November 2011.
- Pavković, Božo (9 January 2012). "Milović novi igrač Hajduka, Glumac u Parku mladeži!". dalmacijanews.com (in Croatian). Retrieved 9 January 2012.