Gülüm grew up in the Melbourne suburb of Meadow Heights.
Career
Gülüm progressed up the ranks after playing exceptional football for Hume City as an 18-year-old. He was originally transferred to Turkish Super League team Manisaspor in 2005, after being spotted by Leading Teams Operations Manager Ezel Hikmet and referred to experienced Turkish coach Ersun Yanal whilst playing for and captaining the Australian School Boys team touring the United Kingdom. Impressed with the raw talent of the young defender, Gülüm was a part of the senior squad for the entire season as a backup defender, but only managed 2 Super League and 2 Turkish Cup matches. Gülüm was transferred to Elazigspor in February 2008 where he managed to play in every match, gaining a reputation as a strong left footed defender. After a solid second half of the season, Gülüm was transferred to Adanaspor for the 2008–09 signing a lucrative three-year deal, where he played 30 League matches and was rewarded for his great form by being selected in the team of the year as the best central defender in the competition. On 17 July 2010, despite being heavily linked with Galatasaray, Gülüm transferred to rival Turkish club Beşiktaş with Adanaspor acquiring an option to loan Gülüm back for one season. After he had a productive season with Beşiktaş, they acquired Gülüm's full rights for a fee of €4 million. On 17 July 2017, Gülüm transferred to Adelaide United on a season long loan from Hebei China Fortune Adelaide United announced that Gülüm had returned to Hebei China Fortune after making 22 appearances on loan to the Adelaide club. In November 2018, Gülüm returned to Melbourne, joining Victorian State League Division 1 side Whittlesea United as player-manager. On 7 May 2019, Gülüm signed for new A-League club Western United for the upcoming 2019–20 A-League season.
International career
Gülüm was born in Australia to Turkish parents, meaning that he was eligible to play for Australia and Turkey from birth as per the FIFA eligibility criteria.
Australia under-23s
Gülüm was involved in Australia's qualifying campaign for the 2008 Summer Olympics, he made his international debut for the Australia national under-23 association football team as an 84th-minute substitute replacing Ruben Zadkovich on 6 June 2007 away to Jordan in Ammam. In November 2010, it was speculated that he would be selected for Australia's friendly against Egypt. After the call-up did not come, Gülüm chose to represent Turkey and said that he often felt overlooked by Football Federation Australia: "For me it has been a case of being overlooked at all levels in the past for Australia, for whatever the reason has been."
Turkey
Former Australia head coach Guus Hiddink swooped and added Gülüm to the Turkish squad scheduled to play the Netherlands on 17 November 2010, although he did not make his international debut for the Crescent Stars in that match. The following month, Australia coach Osieck had met with Gülüm while the Australian men's team was touring Europe and stated that Gülüm was "very positive" about representing Australia. Gülüm was named on the 50-man shortlist for Australia's 2011 AFC Asian Cup campaign, but was not selected in the final 23-man squad. Osieck told the press that Gülüm's father "said Ersan should opt for Turkey because he plays in Turkey and makes his living there and they both feel a lot of pressure from the Turkish media and the Besiktas supporters". Gülüm was again called up to the Turkish national team in November 2012, this time by Abdullah Avcı. He said he was proud to be a part of the national team. He was left off the team on the roster when the team played Romania on 12 October 2012. He was an unused sub in Turkey's 6 September 2013 match against Andorra. He made his first appearance for Turkey as a 90th-minute substitute on 10 September 2013 in a 2014 FIFA World Cup qualifying game against Romania.
