They also say they won't be renewing their contract with the Baffin Fisheries Coalition (BFC) when it comes up for renewal at the end of this year.
There are 500 people in Qikiqtarjuaq and only 25 of them have full-time jobs.
The NHTA has requested a 1,500 tonne Turbot quota from both the Nunavut Wildlife Management Board and DFO.
The quota would be incremental and not affect the 4,000 tonnes of turbot already allocated to the Baffin Fisheries Coalition (BFC).
They hope it will kick-start their own community turbot fishery.
They claim their inshore fishery will create 20 much-needed jobs in Qikiqtarjuaq.
The NHTA has already spent thousands of dollars on its own boats, equipment and trips to Ottawa to meet with federal government officials about their fishery plans.
In a letter made public this week, the NHTA claims that public representatives of the Nunavut Wildlife Management Board (NWMB); Nunavut Tunngavik Inc. (NTI); Olayuk Akesuk, the GN's minister of environment; and Premier of Nunavut Paul Okalik are "constantly refusing to come to our community to explain what is going on" with regards to the Baffin Fisheries Coalition.
They say the representatives are keeping important information from them.
"The benefit of the fishery is not translating to the bottom line in these communities," said Inuk Senator Willie Adams' research assistant Richard Selleck.