Translation:The teachers would have represented the parents, too.
Interesting. In English, though, I'm not sure I'd use "cover for someone" in quite that sense--that is, of formally substituting for someone. I'd be more likely to use it to represent a quick ad hoc action--"Can you cover for me while I run to the store?"
Of course, context is everything, and we have no context here. Still, I can't think of an instance in which someone would say "The teachers would cover for the parents."
We do have a concept of teachers acting "in loco parentis," that is, "in place of the parents," meaning they might have supervisory or disciplinary powers normally allotted parents, but I don't think one would use "cover for" in that case.