Shortly after her trial ended in August, Letby applied for leave to appeal against her convictions.
She lost the first stage of the process, in which a single judge reviewed her arguments as a paper exercise.
Letby, originally of Hereford, now has the right to a second stage, which involves renewing her application before a panel of judges at a hearing at the Court of Appeal.
The nurse is attempting to challenge her convictions on four grounds, which involve arguments that the judge at her trial wrongly refused legal applications made during the case, which lasted for 10 months.
Separately to the appeal, Letby is due to be re-tried on one charge of attempted murder, which the jury at her trial was unable to decide on.
That re-trial is due to commence in June.
As a result, to avoid prejudice, the media will not be allowed to report the full detail of the appeal hearing at this stage.
A public inquiry into events at the Countess of Chester Hospital is also planned, and its first hearings are expected in the autumn.
