Fence Greyhounds in astra Mirach, in Garfilli County, said getting a license would better care for the animals.
But a dog rescue charity fears these programs could lead to more dog injuries and deaths.
The Welsh government stated that responsible animal rights were a priority.
The dog Cyril was maintained by the Hope Rescue charity after suffering a fracture in a foot race.
Hope said Cyril was wounded in the valley.
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But Drake said the dog's owner did charity work for the animal after it was banned from the stadium.
The charity said thousands of pounds had been spent on surgery and rehabilitation for the rehabilitated Cyril.
The Greyhound Board of Great Britain (GBGP) raises concerns that if the fence greyhounds are licensed to race, they will jump from one to four races a week and the dogs will be injured.
These concerns prompted the start of the petition, which will be considered for debate in the Senate.
Hope Rescue owner Vanessa Watten said: “There will be a veterinarian on the kennel, the traffic used and the track, but you will not stop injuries and deaths.
"Actually you will intensify it."
The petition has received support from politicians, including Jane Dots, the leader of the Welsh Liberal Democrats.
Ms. Dots said: “When Arthur, my own Greyhound, was six years old, I saved him because he fell and injured his neck during a race.
"And he's still scarred by the time he's on track. We need to outlaw greyhound racing and not issue licenses."
Hope Rescue claimed to have taken 200 greyhounds from the fence greyhounds, of which 40 were seriously injured, either directly from the track or by those associated with it.
The Valley Greyhounds have denied these numbers, with some animals injured in its path.
According to the Greyhound Board of Great Britain, 3,575 greyhounds were injured and 200 died on the track by 2020 on licensed tracks.
Although the number was lower than in previous years, fewer races took place in 2020 due to the Govt.
Malcolm Toms, former owner and current manager of the Valley Greyhounds, said there have been "massive improvements" in animal care because they are expensive.
"I have seen this kind of petition with 120,000 signatures being submitted to the UK government, and it was decided by the government to allow the game to manage itself under the BGRB or GBGB," Mr Tombs said.
Dave Barkley, the new owner of Fence Greyhounds, did not want to comment on Hope Rescue's plea, but said about £ 500,000 would be invested to meet the GBGP standards.
He said getting the license would boost the local economy.
Mark Byrd, chief executive of the Greyhound Board of Great Britain, said: "This petition does not take into account the very high level of restrictions and scrutiny that exist in Greyhound racing licensed in Great Britain."
Mr Byrd said: "We welcome the application for a license from the Valley because it requires us to maintain our racing rules and to provide the highest level of care to all racing greyhounds."
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