For the first time in more than two years, city principals are being told they can look outside the city’s current teaching corps for new English and social studies teachers.

The deadline for new English, social studies, and math teachers to enter the city’s hiring system has been extended until Monday because “opportunities may exist for schools to hire new teachers in these areas,” according to the Department of Education’s hiring website.

The schools aren’t being given carte blanche to hire teachers externally in those subjects, but they are being told they can apply for exceptions to the city’s two-year-old hiring freeze. In the past, principals have been granted exceptions from the freeze if they could show they had searched exhaustively within the system.

“We are pleased to share that schools may be able to receive an exception” to hire teachers in the subject areas, read an email sent by a DOE official to colleges and universities that supply student teachers.

Principals are responding to the encouragement. In the last week, the DOE’s online hiring system has had positions added by schools that would not previously have been allowed to hire externally under the restrictions.

For example, there are at least 10 middle school English teacher positions currently listed, and some of them — for example, Manhattan’s PS 34 and Brooklyn’s IS 302 — are not new schools, which have always been able to hire some teachers from outside the system.

The recent change offers a clue into the decisions that principals made when allocating their funds for next year. One option to trim spending is to “excess” teachers, or eliminate their position within a school. The city is unlikely to lift hiring restrictions in subjects that saw many teachers excessed. That’s because teachers whose positions are eliminated continue to work in the system, and the hiring restrictions are meant to ensure that open positions are filled whenever possible with teachers already on the payroll. If the city is opening its doors to new English, math, and social studies teachers, then the excess pool is likely to have fewer of them than there are open positions.

Principals had to make decisions about excessing teachers by July 15 and submitted their complete spending plans for the next school year by July 22. So far the city has not released any details about how principals chose to spend their budgets or how many teachers are being excessed.

Some subjects, including special education, science, and English as a second language, have long been exempt from the restrictions. Now the city’s firmest line keeps out early childhood and elementary school teachers, long the most commonly held license among people in the excess pool.