Previous applications were refused by the Judicial Review Court and the Court of Appeal.
In a decision handed down on December 13, the committee said Gorstew’s application does not raise an arguable point of law which would enable the proposed appeal to succeed.
It further said there is no risk of a serious miscarriage of justice by refusing the application.
The law firm Knight, Junor and Samuels represented Lynch and Pyne, while Barber as represented by attorneys Deborah Martin and Sharon Usim.
Lawyers from the Attorney General’s chambers represented Shelly Williams
In 2014, Shelly-Williams upheld a no-case submission freeing Lynch, Barber and Pyne of fraud charges in relation to the ATL pension fund.
They were accused of distributing nearly two billion dollars in interest and surplus to members of ATL's pension scheme without the consent of the company's Chairman, Gordon Stewart.
Gorstew took the matter to the Judicial Review Court seeking to have the decision quashed and the matter retried.
The company lost the case but pursued the matter in the Court of Appeal, which also ruled against its application.
Gorstew then applied to the judicial committee of the Privy Council seeking leave to bring an appeal but the application was refused.