彼はもう英語を教えるまい。 (Most probably, he won't teach English any more.) I got this sentence from this thread. もう doesn't seem necessary to use or have. Isn't the meaning the same if it was like this: 彼は英語を教えるまい。?
In this case もう gives the meaning "any more". Without it, the sentence would mean:
Note that 教えるまい has the same meaning as 教えないだろう. The latter form is more commonly used but the former is still used in writing sometimes.