Translation:She will be responsible for the communication area.
I´ve occasionally heard responsible used as a noun in American English, meaning responsible party or responsible officer. In the context of this sentence, "She will be the responsible (officer) for communications."
However this usage is uncommon, and a quick google search didn´t yield any dictionary references that would support it being technically correct.
Ah, so ‘a responsável’ is ‘the one responsible’. That makes sense.
But when you're e.g. dividing tasks you'd leave out ‘the one’ and simply say ‘She'll be responsible for ...’.
Still, I just did some web searching and even in Portuguese it seems to be more common to leave out ‘a’.