The Helen Suzman Foundation (HSF) has filed an urgent application to have the court order, to set aside Hawks boss Berning Ntlemeza's appointment, executed.
In its application filed on Monday, the HSF argues that the application for leave to appeal cannot suspend the order by the North Gauteng High Court in Pretoria.
"The order continues to be operational and enforceable and will operate and be executed in full until the final determination of all present and future leave to appeal applications," it said in court papers.
Both Ntlemeza and Police Minister Nathi Nhleko filed applications for leave to appeal against last Friday's ruling by the High Court in Pretoria that found Ntlemeza's appointment as Hawks head unlawful and invalid.
Judge David Mabuse found that Nhleko had ignored two earlier judgments by Judge Elias Matojane when he appointed Ntlemeza head of the elite police unit. He added that Ntlemeza lacked integrity and honesty.
HSF argues that its application is a matter of urgency and cannot be overstated.
It adds that the reasons for its urgent application are compelling, as a review court has determined that Ntlemeza's appointment be set aside.
"The national head is at the very heart of the Directorate for Priority Crime Investigation's (DPCI) ability to function effectively to fulfill its constitutional mandate. It is clearly the case that an application which attempts to prevent irreparable harm to the DPCI ... should be determined as soon as possible."
'Devoid of evidence'
In his application to appeal Mabuse's ruling, Ntlemeza argues that the court failed to consider his written responses to Matojane's comments.
"It is respectfully submitted that another court could come to a conclusion that the pronouncement by Judge Matojane in both judgments about alleged dishonesty and impropriety were with respect devoid of evidence placed before him and therefore inappropriate."
HSF and Freedom Under Law had brought the application, asking the court to refer the appointment back to a selection panel for a new candidate to be chosen.
In January 2015, Ntlemeza suspended Gauteng Hawks head Major-General Shadrack Sibiya for his involvement in the alleged illegal rendition of Zimbabwean prisoners in 2010.
Sibiya challenged the decision in the High Court and won. Ntlemeza applied for leave to appeal against the judgment.
In his ruling, Matojane found Ntlemeza had withheld information from the court and police watchdog, the Independent Police Investigative Directorate, which could have enabled the court to make a proper assessment. He found Ntlemeza lacked integrity and honesty.
In his application for leave to appeal, Nhleko said Matojane erred in relying on the Sibiya judgment.
"The full court erred in relying on the remarks made in the Sibiya judgment since such remarks were made without the second respondent [Ntlemeza] having been afforded an opportunity to deal therewith."