Only a small number of teachers will strike, a spokesperson from the day and boarding school says.
The industrial action over union recognition had been running at four Horncastle schools since May.
All five of Northern Ireland's teaching unions will take part in the action from Monday, 28 September.
Wales' largest teaching union is calling for a national ban on phones in schools.
Northern Ireland's five teaching unions voted for industrial action if their grievances concerning workload were not addressed.
In recent ballots the five main teaching unions received large majorities in favour of industrial action.
A dispute in Lincolnshire over jobs and workload remains unresolved ahead of the new school year.
The new plan to save money will not involve restructuring or compulsory redundancies, a union says.
Union members end their industrial action at Haydon Bridge High School amid talks with new bosses.
