Henrik played schoolboy football for
Fulham and
Reading. He was released by Reading in the summer of 2009 and joined
Aldershot Town's academy. He has also played for the club's reserves. After impressive appearances for Aldershot's youth and reserve teams, Henrik was given a trial by
Chelsea's academy in February 2011, playing against the academy sides of
Portsmouth,
Birmingham and
Milton Keynes Dons. Breimyr was runner-up in the 2011 League Two Apprentice of the Year, and signed a professional contract with Aldershot in April 2011 that tied him to the club until 2013. In February 2012, Breimyr joined the Norwegian side
Viking on a one-year-long loan deal. He made his debut in
Tippeligaen against
Haugesund on 28 April 2012, when he replaced
Christian Landu Landu as a substitute in the 55th minute. Breimyr spent most of the first half of the season playing at
Viking's reserve team in the
Third Division, and the loan-deal was terminated on 3 August 2012 by mutual consent. Instead Breimyr was loaned out to
First Division side
Bryne on 22 August 2012. Breimyr left
IL Hødd at the end of the 2018 season. ==International career==