It also prohibits the ability for clubs to merge machines when amalgamating, such as the when the Napier Cosmopolitan Club and the Taradale Club merged in 2012.
The council's existing policy of a cap of two TABs in Napier remains.
Mayor Kirsten Wise said she is pleased with the outcome of Tuesday meeting, which she says struck "the right" balance between restraining the increase in problem gambling and its effects on the city of Napier, while ensuring there is no immediate impact on businesses or reduction in grants available to fund charities and community projects.
The council had received 105 submissions and during the meeting, the mayor and councillors acknowledged the "passionate" input of most of the 20 people and organisations who appeared.
Opponents of the machines generally stressed they were not opposing gambling as a form of recreation or entertainment, conceding that even they had taken the odd wager on the Melbourne Cup, but it was clear there was a gambling harm problem with some, and it had a disproportionate impact, the councillors said.
Wise said "the big issue" was that the gaming venues and their machines were only licensed to fund charitable causes.
The council is among the recipients, getting tens of thousands of dollars every year.
She suggested the council submit a remit to councils network Local Government NZ to urge the Government to develop an alternative funding stream to remove the need for support from the proceeds of gambling.
The council is also likely to review its own "relationships" with the gaming funds trusts that distribute the grants.
She said late Wednesday council staff had already been instructed to work on a remit she expects to be put to the council at a meeting on April 22, to go to the LGNZ to operate as a collective to lobby Government, or for the council itself to lead the debate.
Gambling has been used to raise money for charitable purposes in New Zealand for more than 130 years, dating back at least the first Art Union lottery run by the Otago Art Society in 1877.
The Art Union was the forerunner to the 1961 introduction of the Golden Kiwi, a nationwide lottery eventually drawn at least once a week. The name lives on in Instant Kiwi scratch cards, run by Government agency the New Zealand Lotteries Commission, which established Lotto in 1987, when pokies were also introduced to pubs and clubs throughout the country.
Opponents of the machines claimed at Tuesday's hearing that Napier has one of the country's greatest spreads of machines per head of population.