[1][2] Skrobić started playing handball at age 14 after first practicing Aikidō.
[3] She started at ŽRK Zemun and later joined RK Junior.
[4][5] In the summer of 2015 she joined Montenigrin club ŽRK Budućnost Podgorica.
[7] She also reaching the final four of the EHF Champions League with the club.
[5] Two years later she joined league rivals Érd HC.