[1] Ingvar has acted extensively in film, television, and stage productions, both in Iceland and overseas.

He had roles in Friðrik Þór Friðriksson's Englar alheimsins (Angels of the Universe) and Baltasar Kormákur's Mýrin (Jar City)[2] and Everest.

[3] Ingvar became internationally known for his role as police officer Ásgeir in the Icelandic TV series Trapped (2015–18).

[4] He has collaborated with Icelandic director Hlynur Pálmason on several occasions, from his graduation short film in Denmark, A Painter (En maler), in 2013, his second feature film A White White Day,[5] and in 2022, Godland (Icelandic: Volaða land, Danish: Vanskabte Land).

[6] Ingvar has won the Edda Award for Actor or Actress of the Year four times, for his performances in the short film Slurpinn & Co.; and the feature films Englar alheimsins (Angels of the Universe); Kaldaljós (Cold Light); and Mýrin (Jar City), in 1998, 2000, 2004 and 2006 respectively.