After several years working as an administrative support person at my company, I have a new job in a different area of our department, which is completely different and has no administrative duties.

One Director (out of 8) in our department continues to e-mail me to do administrative tasks, even though she knows I have a new non-administrative position.

My Director says that he's mentioned this to her, but the Director continues to send me/ask me to do various duties.

I want to make two things perfectly clear: one, There are six administrative staff in my department of 400, and there is not anything that I did, that they cannot do. Two: the person who previously held my job did not have to do any administrative tasks (again my new job is not even remotely administrative in any way).

I don't want to be seen as not being a team player, but I don't think I should be doing MY job and my OLD job, esp. when there are people who can do whatever tasks she requires.

Should I go to H.R ?

Yes. I'd be prepared, however, to be told you aren't a team player and then it's up to the people in charge.

Contract or union?

Who do you report to, Have you went and talked to this person about this not being your duty any longer?