(Assuming you are playing the original trilogy and not BT4)

I believe the game will tell you if you try to acquire more spells without changing class.

In any case, once you're level 13, you can learn level 7 spells in the class, and level 7 is the highest level, so once you learn those spells, it's time to change class.

Note that, in some versions of the first 2 games, the later spellcasters level up *really* slowly, so if playing one of those versions, you may want to plan on ending your casters as Conjurers or Magicians (so that you need only 230k XP per level past 13 rather than the 1.3 million a Wizard requires in those versions).