[2] Paulsen made his debut for SønderjyskE in the Superliga during the 2009–10 season, coming on as a late sub in a 1–3 away loss against Nordsjælland on 25 April 2010 at age 19.

[7] On 24 October 2012, starting at striker in a 4–0 win over lower-league side FC Hjørring (now Vendsyssel FF) in the Danish Cup, he scored his first career hat-trick.

[14] Paulsen started out playing as a central defender, but in October the same year, Esbjerg appointed Jonas Dal as their new manager.

[16] In total, Paulsen made 25 league appearances in the campaign, scoring three goals, whilst being an important member of the Esbjerg squad.

Paulsen was named as one of five players that could be deemed surplus to requirements at the club during the January transfer window, due to his reportedly high salary.

[20] On 9 April, he scored his first competitive goal for Hammarby, a late equalizer as his side drew 1–1 against Kalmar FF on the second matchday of the league campaign.

[23] Throughout the season, Paulsen played 29 league games and scored eight goals in total, being voted Hammarby Player of the Year for 2017 by the supporters of the club.

[24] In August 2018, following a number of impressive performances in the central defender position, Paulsen attracted interest from AEK Athens.

[26] He was nominated for the prize Allsvenskan defender of the year, that eventually was awarded to Per Karlsson,[27] and chosen as one of the eleven best players of the season by Cmore Sports, Fotbollskanalen and Playmaker.

Bundesliga, Paulsen played 16 games and scored twice, as Ingolstadt finished 16th in the table and lost the relegation playoff against SV Wehen Wiesbaden on away goals.

Liga season, Paulsen made 30 league appearances for Ingolstadt, as the club qualified for the promotion playoffs but lost to FC Nürnberg on away goals.

[34][35][36][37] Paulsen featured in the final of the 2021–22 Svenska Cupen, in which Hammarby lost by 4–5 on penalties to Malmö FF after the game ended in a 0–0 draw.