First Buxton signings as new boys reunite with boss Craig Elliott
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Jordan Burrow is a centre-forward while Luke Shiels is a central defender.
Striker Jordan Burrow, six feet one tall and a product of Chesterfield's youth system, has played in the EFL for Morecambe and Stevenage and is an England C international.
Experienced defender Shiels, 33, from Sutton-in-Ashfield, was Boston's player of the year in season 2019/20 and more recently club captain. Previously, Luke was with Alfreton Town, Harrogate Town and Worksop Town. He played against Buxton twice last season.
The pair are the first summer signings as Craig Elliott prepares for the new season in the Vanarama National League North.