Following the outbreak of the Bosnian War, Obuća volunteered for the Army of the Republic of Bosnia and Herzegovina, serving in Goražde.

Her team achieved notable success, including a third-place finish in the national championship and participation in the EHF Cup.

After this period, she held the position of head of the department for legal and economic affairs at the Public Enterprise Bosansko-Podrinjske šume (English: Bosnian-Podrinje forest agency).

[7] In 2019, Obuća was elected Premier of the Bosnian-Podrinje Canton Goražde, the first woman to hold this position[8] in the Federation of Bosnia and Herzegovina.

During her tenure, she focused on financial stability, social welfare,[9][10] anti-corruption measures, and infrastructure development.