"With the accession of King James, this policy came to an abrupt end, and with it a tradition of representing formidable, eloquent and savage Turks, Moors and Persians on the Elizabethan stage. They would be reinvented in a different key by a new generation of Jacobean playwrights." (Jerry Brotton, This Orient Isle- Elizabethan England and the Islamic World)
It is a musical metaphor. A piece of music written in one key assumes a different nature and colour when transposed to another key: same theme but different expression. The metaphor suggests that the depiction of "Turks, Moors ..." by the new playwrights who came after James became king was different in some way from that made previously.