Kolbrún Björt has written four original full length shows, Kjöt (e. Meat), Bitter Sweet, Chet Baker, Love and ​(Can This Be) Home all produced by Brite Theater. Her writing has been described as stripped back, clever and bold. (Can This Be) Home won the New Territories Award at Prague Fringe 2018. Her short play Snow was chosen for Winter Words Festival 2017.

She has adapted Shakespeare's Richard III and Hamlet (with Emily Carding) and Twelfth Night (with ensemble) as well as Chekov's The Seagull. She has also adapted four musicals, both story and songs. She translated Howard Barker's Knowledge and a Girl into Icelandic. 

Her original Shakespeare mash-ups, My Only Love Sprung from My Only Hate and Shakespeare in Hell (with Emily Carding) have been renowned for providing new insights into the Bard's characters. 

She worked as a dramaturg on Gareth Morgan's Notes on Some Persons, Starting to Crack and assisted dramaturg Marc Matthiesen and director Egill Palsson on their adaptation of Frun från havet for Göteborgs Stadsteatern (Gothenburg's City Theatre). She is currently working on ​The House That Melts with the Rain​ by Jennifer Adam, ChildMinder and Tulla by Iain McClure and Knots with Theatre Sans Accents.

​Her piece ​Troubles of the Female Variety​ was chosen and performed as part of Words Words Words at the Traverse Theatre in 2016. Kolbrún is currently working on expanding this following being a mentored playwright at Playwrights' Studio Scotland, mentored by Alan McKendrick. She is also writing a new play for an ensemble called Where Exactly which saw it's first staging (excerpt) at the Tron 100 Festival 2017 and got a second outing at Stage to Page October (excerpt), curated by Douglas Maxwell.