"They prefer to employ hearing people because they have more skills, rather than upskilling Deaf people," Leach told the Herald exclusively.
"They don't understand, they can't build rapport; they don't know Deaf culture, habits and language. It feels disrespectful.
"We feel like we've been kicked out. We feel like we've been elbowed out of the way."
She compared it to hiring a Pakeha boss for a Maori organisation.
"You wouldn't hire a Pakeha CEO."
Around 380,000 Kiwis are affected with a hearing impairment of which 11,000 use New Zealand Sign Language as their primary form of communication.
Deaf artist Abbie Twiss was sick of seeing tokenism where a few Deaf people were recruited so the organisation looked diverse, but these people never make it into management.
"In the hearing-led environment there's a 'hearing superiority' that Deaf people really feel," Twiss said.
"We want NZ Sign Language to be celebrated, not to be used for charitable purposes to make money."
Lachlan Keating has been Deaf Aotearoa's chief executive for five years. He is hearing and said he has a conversational level of sign language. He uses interpreters every week for complex situations, or people he doesn't know well.
Keating believed Deaf leadership had improved under his management. He said of his 76 staff, 41 and half of his 14 management staff were deaf and over the last two years they had put 25 Deaf people through qualifications.
Keating was appointed by the board of trustees who are all deaf.
"There's never been more Deaf managers and Deaf leaders than now," he said
"If they are highly skilled and experienced I would have grabbed them [Deaf people], they are like fairy dust."
Keating believed hearing chief executives were appointed "because they're the right person for the job at the time." He said if a particular job or situation required a Deaf person he would give that job to them.
"For the last five years Deaf Aotearoa has never been stronger in every aspect."
Acting chief executive of Kelston Deaf Education Centre Tom Purvis, who is hearing, said around 20 per cent of their 195 employees were deaf, with a similar proportion in management.
The Auckland Deaf Society refused to comment on how many deaf people they employed, whether their chief executive Fiona Brennan was deaf or if she has a sign language qualification.
Leach said one reason Deaf people weren't chosen was because they were often less qualified than a hearing person.
The average Deaf person has a reading age of 9 to 12 when they leave school. This makes it difficult to pursue a university education and gain qualifications.
Green MP Mojo Mathers, who is one of only five deaf MPs in the world, said it shouldn't be left to a "tiny handful" of organisations to meet employment aspirations for Deaf people. Instead she believed all organisations needed to take responsibility.
"Currently it is very clear that Deaf people in New Zealand face significant barriers to employment or career development.
"Across all sectors there are very few opportunities for Deaf people to upskill, develop careers or take up senior positions of responsibility. This is a systematic problem that will take significant commitment to address."
Deaf facts
• Statistics NZ found a hearing impairment affected 380,000 people (9 per cent of the total population).
• New Zealand Sign Language is one of three official languages in New Zealand, along with English and Te Reo Maori.
• NZSL has its own grammatical structure which enables users to communicate fully and express thoughts and emotions.
• There are approximately 11,000 deaf people who use NZSL as their primary form of communication and approximately 20,000 people in total who use NZSL. This includes parents who use NZSL to communicate with their deaf child.