Tharme started his career progressing through the academy at Wrexham and made his professional debut for the North Wales side in 2018 in a 2-2 home draw to Bromley in the National League. He then went on to make a further three appearances that season for the Red Dragons.

The following season he signed for AFC Telford on loan and made one appearance. At the end of 2019 the defender signed for Tamworth and made one appearance before being transferred to Curzon Ashton on a permanent deal where he made 12 appearances in all competitions.

After securing another permanent transfer to Welsh Premier League side Connah’s Quay Nomads, where he went on to make four appearances, the 24-year-old then made the switch to Southport in the summer of 2021.

At Southport, Tharme made 32 appearances all season, scoring 3 goals which earned him a transfer to League One side Blackpool in the January of that season, but the defender returned to Southport on loan for the remainder of the season.

For the entirety of the 2022/2023 season, Tharme was loaned out to Accrington Stanley where he made 37 appearances across the FA Cup, EFL Trophy and Sky Bet League One.