Either is correct, depending on what you mean. It is not so much an issue of using a subordinate clause as whether you are reporting speech. She told me that she is a teacher clearly means that she is a teacher now. However, it is common in English in reported speech to change the tense to the past. So, if she said, "I am a teacher," it is correct to say, "She told me that she was a teacher." And if she said, "I was a teacher," you could say, "She said that she had been a teacher."

The past tense "was a teacher" can be interpreted in two different ways: - she was a teacher in the past, but is no longer one - the person was told in the past that this person is/was a teacher Technically speaking, the tense of "is/was a teacher" should match whether or not she is a teacher now or not. But I agree with the other poster that it is common in this type of phrase to change the tense of the verb "is/was" in this clause to match the tense of "told", which would be past tense.