[1] Akgün started her handball career at her hometown club Muratpaşa Bld.
[24] In May 2021, she transferred to the newly formed club Ankara Büyükşehir Belediyesi EGO SK.
[26] Her team was the runner-up in the 2022–23 Women's Handball Turkish Cup ("2022–23 Kadınlar Hentbol Türkiye Kupası").
[32] She played in the 2015 World Women's Handball Championship – European qualification.
[33] In 2017, she won the silver medal with the national team at the Islamic Solidarity Games in Baku, Azerbaycan.
[34][35] She took part in the Mediterranean Games in 2018 in Tarragona, Spain,[3] and 2022 in Oran, Algeria,[36] in the European Women's Handball Championship qualifying in 2018,[37] 2021,[32] and 2022.
[39][40][41][42] In August 2021, she was honored by the Hentbol Haber with the Bests of Handball award for her successful appearance as pivot in the 2020–21 Turkish Super League.