The TNRL was expelled from the IRL in March last year, after a long-running battle over governance, money and a threatened player boycott.
The hearing between TNRL and the IRL was held on 8-to-9 December 2020.
CAS Communications Officer, Katy Hogg, told Matangi Tonga that it is unknown when a decision will be announced.
Two separate organizations have applied for full membership with IRL to become Tonga's recognized national rugby league governing body since TNRL's expulsion.