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He will replace George Roach, who will remain on as CEO.
Roach said the separation of the two roles was "long overdue" and should enhance board oversight and direction.
Foster has been on the Premier board since 2015 and was previously non-executive chairman of Copperbelt Minerals.
He said his focus would be on "strategic governance, improving all aspects of board oversight and assisting management meet targets and advance the Zulu lithium project, as well the RHA tungsten mine in Zimbabwe".
