[1][2][3][4] Haugsted started playing handball at the age of 10 at Skive fH.

In 2010 she switched to FC Midtjylland Håndbold, where she played for two years before returning to Skive fH.

After three seasons where she broke through to the first team at Skive fH, she signed a three-year contract with Odense HC.

[8] On 30 January 2022, it was announced that Haugsted had signed a 2-year contract with Hungarian top club Győri ETO KC.

After a little more than a year, she returned to Danish handball to join Team Esbjerg.