Nartey penned a deal with the Clarets in November 2020.
The London-born defender came through the academy system at Stamford Bridge, where he played alongside Declan Rice, Tammy Abraham, Reece James, Callum Hudson-Odoi and Mason Mount.
The Wimbedon-based defender was part of Chelsea’s FA Youth Cup-winning side in 2016/17 before earning a professional contract with the Londoners.
And the 22-year-old, who made 29 appearances for League One side Burton Albion last season on loan, was then released by the Blues in the summer of 2020, before joining the Clarets.