Anne of Cleves never remarried after the annulment because, like Catherine of Aragon, she believed that she was Henry's true wife, so much so that she believed that they would remarry after Catherine Howard's fall.
Convocation had declared in 1540 that Anne was free to remarry but Elizabeth Norton points out that nobody would have dared to marry the king's ex-wife while Henry was still alive and also Anne believed herself to be Henry's wife. Even after Henry's death, there is no evidence that Anne ever considered remarriage but Edward VI did recommend her as a wife to Thomas Seymour.
It is true that a remarriage would have made Anne dependent on her husband and not the King's council but although it is often said that the terms of the annulment forbade her from remarrying, this is not true.