Olhaver played as a youth in his native Sweden, within the Rögle BK junior program. Possessing a towering frame, Olhaver played parts of two seasons in the J20 SuperElit, producing 12 points in 41 games throughout the 2014–15 season. Showing glimpses of offensive touch, Olhaver was drafted in the seventh round, 191st overall, with the Colorado Avalanche's last selection in the 2015 NHL Entry Draft. With intention's to pursue a major junior career in North America, Olhaver joined the Avalanche's rookie camp and was selected 44th overall in the 2015 CHL Import Draft by the Seattle Thunderbirds of the Western Hockey League. On July 1, 2015, Olhaver agreed to terms to join the Thunderbirds for the 2015–16 season. While aiming to develop his offensive game with his physical play, Olhaver struggled to make an impact and was placed on waivers by the Thunderbirds and later picked up by the Swift Current Broncos on December 28, 2015. Olhaver played out the season with the Broncos, finishing the season with a combined 8 points in 51 games. On May 27, 2016, Olhaver opted to return to the junior ranks with Rögle BK. In the 2016–17 season, while enjoying a productive return to the J20, Olhaver made professional debut in the Swedish Hockey League with Rögle BK. He featured in 10 games in recording 1 assist. Having graduated from the under-20 level, and with a roster position limited with Rögle BK, Olhaver left the club to sign a one-year contract with second tier outfit, IK Oskarshamn of the HockeyAllsvenskan on April 24, 2017. In the off-season, he attended his third training camp with the Avalanche, before returning to begin the 2017–18 season with Oskarshamn. In his first full season in the Allsvenskan, Olhaver earned a regular role amongst the forwards, contributing with 6 goals and 13 points in 48 games. After a post-season exit, Olhaver left Oskarshamn opting to continue in the Allsvenskan on a two-year contract with Tingsryds AIF on April 16, 2018. In his final season under contract, Olhaver established himself within Tingsryds, recording professional highs with 13 goals and 22 points in 47 games. He played a solitary game in a return to the SHL, with original club, Rögle BK. On 27 March 2020, Olhaver signed a one-year contract with MODO Hockey to continue in the Allsvenskan.
