Captain of the Under-18s during the 2020/21 season, midfielder Oliver Green signed his first professional deal with the club in May 2021.

In July 2021, Green featured in the first-team’s pre-season friendlies against Mansfield Town and Manchester United, and was also an unused substitute in the Tigers’ EFL Cup fixture against Wigan Athletic in August 2021.

In March 2022, Green experienced his first career loan spell as he joined Bridlington Town. He helped the Seasiders stay in the Northern Premier League East Division, making five appearances, and was rewarded a new contract with the Tigers in May of the same year.

In November 2022, Green joined Marske United originally on a one-month loan before extending his time there by a further month. Under the management of former Hull City midfielder Curtis Woodhouse, Green registered five assists in seven appearances for Marske, helping the Seasiders reach the third round of the FA Trophy for the first time in the club's history.

Captaining the Under-21s on a consistent basis and featuring as a substitute for the first team in their pre-season friendly against Ligue 1 side FC Nantes, the midfielder went out on loan to York City. Playing eight games for the Ministermen, Green played over 500 minutes for the club.