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First Nations people living in "dilapidated" housing in the Northern Territory could be compensated after Australia's highest court agreed to hear their case.

Eastern Arrernte woman Enid Young is pursuing legal action against the NT government over the poor quality of rental homes in the remote community of Santa Teresa in central Australia, near Alice Springs.

Residents have been left without electricity, hot water, cooking facilities or functioning toilets for months and years at a time, according to not-for-profit litigators Grata Fund.

The High Court on Friday granted Ms Young, who is aged in her 70s, special leave to appeal a previous decision by the NT Court of Appeal that tenants could not be compensated.

It will be asked to decide whether residents of Santa Teresa are entitled to compensation for the "distress and disappointment" of living in poorly maintained homes.

Grata Fund said Ms Young had endured more than five years with an empty external doorframe to her property.

Another tenant, a young mother, had been forced to wake up multiple times a night to mop up leaking sewage.

Solicitor Dan Kelly, from Australian Lawyers for Remote Aboriginal Rights, said communities across the Territory were closely monitoring the case.

"The Court of Appeal found the NT government has a legal duty to provide people with a standard of housing that is not only safe, but reasonably comfortable, judged against contemporary standards," he said.

Residents had waited more than six years for the matter to be resolved and one of the lead plaintiffs had died during that time, Grata Fund said.

The group's executive director Maria Nawaz said a remote rent framework introduced by the NT government earlier this year would result in increases for two thirds of renters, "no matter the dilapidated state of the house".

The NT government in late-June cancelled almost $70 million in rental debt for remote Indigenous communities amid allegations the housing was not up to scratch.

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