The quick answer is NO.
The Narok County Government, office of the Governor announced on 5 June in an official press release that the use of private vehicles for game drives in the Maasai Mara National Reserve is prohibited
Only safari vehicles accompanied by a proficient guide are allowed for game drives inside the park.
The park administrator has seen this necessary due to cases of misconduct, off roading and to limit environmental degradation.
This new directive is why you need to hire an official guide chauffeured vehicle to be allowed to enter the Maasai Mara National Reserve. Kenya official safari guides have a TRA license. Make sure you check this before you rent a car to go on safari in the Maasai Mara.