Nairne said she was "deeply disappointed" when she found out.
"In my opinion, there is never any justification for dangerous driving. It is uncalled for and it puts others at risk. As a road safety authority, we spend a lot of time educating the public about this, and we would expect staff would follow the rules more than most."
She said the senior leadership team received monthly reports from the GPS devices in fleet cars, showing where they had been and when, speeds, idle times and trip distances.
Nairne said she did not know how long the cars were travelling at those speeds.
"In the records, if a speed is reached for around three seconds it can be an overtaking manoeuvre."
She said the council took safety "incredibly seriously".
"As a responsible employer health and safety is paramount, but we condemn any law breaking regardless of what it is."
Road safety messages were circulated to council staff after the incidents, and Nairne said follow-up action would continue.
She said in her opinion, GPS devices were a "great" tool for the council fleet vehicles.
"They benefit us in a number of health and safety aspects and speed is just one. We can also use them to locate our staff when they are out and about if we need to for safety reasons... All staff are told about the GPS devices in our vehicles when they sign the council vehicle use policy. They have to be told, under the Privacy Act."
Nairne also confirmed comments made by the council's chief executive Gareth Green on the matter.
"Clearly 150km/h is not tolerable and, clearly, if it was more around 105km/h or 103km/h, then it would be having quite a different conversation," Green said.
Green said he had not taken the figures to police.
"Police have to clock you on their own gear. And my role isn't around enforcement of the road rules, that is the police's role."
Green would not confirm if the staff members driving at 151km/h were still working at the council.
Taupō mayor David Trewavas said he was "extremely disappointed but satisfied the matter had been deal with".
In a written statement, a police spokesperson said: "Speed enforcement action cannot be taken by police based on in-car GPS readings".
"In circumstances such as those described, they can certainly provide a good platform for action by an employer. As well as road safety outcome considerations, that employer action should incorporate obligations under Health and Safety at Work legislation."