Gjelsvik has specialized in the areas of disengagement, radicalization- deradicalization and reintegration of members of armed groups. She has conducted extensive fieldwork in Somalia focusing how individuals engage with and disengage from al-Shabaab and piracy groups. She is currently working on a project on community based policing as a tool for preventing and countering violent extremism in Somalia, Kenya and Norway.

Gjelsvik works at the Norwegian Institute of International Affairs (NUPI) in the Peace and Conflict Research Group. She also works closely with Professor Tore Bjørgo at the Center for Research on Extremism at the University of Oslo and the Norwegian Police University College on research projects focusing on right wing extremism and anti-Islam movements in Norway. She has a master from the Center for Peace Studies at the University of Tromsø with her thesis “Women, war and empowerment: A case study of female ex-combatants in Colombia”.