He is Middlesbrough's seventh signing of the summer, following Alfie Jones, Callum Brittain, Abdoulaye Kante, Sontje Hansen, Sverre Nypan, and Adilson Malanda. Middlesbrough is currently second in the Championship, having won all three of their opening games.

Targett made his Champions League debut in the 2023/24 season and played for Newcastle's manager Eddie Howe in preseason, scoring in a friendly against Espanyol.

As a backup player at Newcastle, Targett decided to leave the team after talks with Howe. A Newcastle statement wished Targett well during his time at Middlesbrough.