Conor Mc Gregor's friend James Lawrence is also appealing a decision not to award him costs, after he was found not to have assaulted Ms Hand by the civil jury.
Straffan Resident Conor Mc Gregor has asked the Supreme Court to hear an appeal over a civil High Court jury finding that he assaulted Nikita Hand.
In July, the Court of Appeal rejected an appeal by the former MMA fighter against that finding by the jury he raped her in a Dublin hotel in December 2018.
His new lawyers have now sought permission from the Supreme Court to hear an appeal.
Conor Mc Gregor's friend James Lawrence is also appealing a decision not to award him costs, after he was found not to have assaulted Ms Hand by the civil jury.

Kfm Obituary Announcements (Saturday)
Sharp Rise In M9 Collisions With Garda Call-Outs Up Year-On-Year
Councillor Seeks Clarity On How Often Nightclubs and Late Bars In Naas Are Inspected For Fire Risks
Unpaid Eight-Month Work And Training Placement For Adults With Disabilities Branded "Extremely Unfair"
Department Of Education Defends Kildare SNA Cuts Amid Claims Of Reduced Need At Some Schools
Naas Nurses Threaten Escalation As Staffing Row Deepens
Driving Tests Face Disruption As RSA Testers To Strike Next Week