Either one is correct:
- For most children, education begins when they enter comprehensive school or traditional grammar school.
- For most children, education begins when they enter a comprehensive school or a traditional grammar school.
They are almost completely equivalent.
Having the word "a" there might remind the reader (or suggest) that there was a choice of different comprehensive schools or different traditional grammar schools, from which one was selected. But this is secondary to the main point of the sentence.
This meaning, or sense of the word a is not certain -- it is one possible interpretation -- so you can consider this to be ambiguous, and you can consider the two choices to be exactly the same.