A 41-year-old Hobart man who tattooed "family" across the cheek of a 17-year-old girl as her mother watched on has become one of the first people convicted under a state law banning under-18s from getting tattoos or body piercings.

Amendments to the Police Offences Act introduced a month earlier made it illegal to tattoo people under 18.

The maximum penalty for tattooing an underage person under the new laws is a $14,000 fine or one year in jail.

The Magistrates Court in Hobart heard Ricky Lawrence Howard had been running an illegal tattoo parlour in the garage of his Bridgewater home.

The court heard he was questioned by police after an anonymous tip-off about the tattoo to Crime Stoppers.

Howard, who tattooed the word "family" across the girl's cheek in January 2015, told the court he had first tried to talk the girl out of it.

But the father of three admitted he had previously tattooed "never run faster than your guardian angel can fly" along the same girl's jawline.

The court heard Howard had tattooed the girl at least three times, the first in 2014.

Girls mother had 'equally evil markings'

The girl's mother had been with her each time.

"Why would a mother allow her attractive daughter to have tattoos on her face?" Magistrate Chris Webster asked.

Howard's lawyer Steven Chopping replied: "The mother had equally evil markings on her, for want of a better term."

Howard claimed he had not realised she was not 18 and that he was unaware new laws made it illegal to tattoo her.

Mr Webster told the man that ignorance of the law was no excuse, and if he was holding himself out to be a tattooist he needed to know the law and keep abreast of any changes.

The magistrate asked whether the teen was happy with the tattoo.

A member of the public called out from the gallery that she was and the prosecution did not suggest that the girl was unhappy with the results.

Mr Webster fined Howard $750 for the illegal tattoos, saying the fact the girl was only three months away from being 18 and the presence of her mother were mitigating factors.

"The laws have been passed with good reason, so young people don't get tattoos as teenagers that they later regret," he said.

"It should be brought home to tattooists that the law is to be obeyed."

Howard was also convicted of running an unregistered and unlicensed premises and a number of firearm offences.