I have notified the Lady Chief Justice about my petition, but I have not had a response

So, here is what I recommend in the meantime:

If you are in the unfortunate position of having your legal matter heard by Judge Noel Kelly, in the Industrial Tribunal, I recommend that you ask Judge Kelly to recuse himself until the PSNI has examined all evidence related to the 2021 Misconduct in Public Office PSNI investigation opened in relation to his conduct by Musgrave CID.

In Northern Ireland there are 3 appeal court judges

Lords Justices of Appeal (3)
The Honourable Lord Justice Treacy (appointed 08 November 2017)
The Right Honourable Lord Justice McCloskey (appointed 05 September 2019)
The Right Honourable Lord Justice Maguire (appointed 08 January 2021)

See: https://www.judiciaryni.uk/about-judiciary/judicial-members

If you have a legal matter being heard in the NI Court of Appeal, your solicitor should ask the judge to identify whether he was the subject of this 2021 Misconduct in Public Office PSNI investigation opened in relation to his conduct, and then he should be asked to recuse himself until PSNI examine all of the relevant evidence.