Staff at Launceston Grammar School will not take industrial action and have accepted improved pay under a new Enterprise Bargaining Agreement.
The move coincides with an indication by the school's board to the union that they would continue to back Headmaster Richard Ford, despite two no-confidence motions this year.
Industrial action, sanctioned by the Fair Work Commission, would have been the first in the history of the 174-year-old school.
IEU assistant secretary David Brear said staff had voted to accept the offer which would put them on a similar salary level to teachers in government schools.
The IEU had been in negotiations with the school since a proposed agreement in late 2018 was voted down.
He said that staff still had some concerns about Mr Ford's leadership.
Under the improved offer the school agreed to set up a consultative forum which would provide staff with the opportunity to have a say on planning and change.
"Staff identified a very top down approach to decision making and poor communication as major problems under the leadership of Mr Ford," he said.
"In an IEU survey, 100 per cent of staff said that school culture and goodwill were being eroded and that the main cause was the leadership of the Headmaster.
Mr Brear said the members cared about the school and the work they did.
"They quite reasonably expect that their opinion about how that work is done will be listened to," he said.
"The industrial action was never about money, it was about being respected at work and that was essentially the same thing that motivated the no confidence motions in the Headmaster," he said.
Mr Ford wrote to staff pledging to improve his style of communication and consultation saying that he had "listened and learned".
"When negotiations on these EBA's began, the school wouldn't even admit that there was a problem," Mr Brear said.