I am separated but not yet divorced from my husband, can I apply for a partner visa with my new partner?

Yes you can, provided you have evidence that you are in a de facto relationship with your new partner, and you otherwise meet the partner visa requirements. In most cases your partner visa application will not be granted though until you provide the Department with proof of your divorce. The DHA may grant a Partner Visa to a person whose marriage has not been legally terminated, where the visa applicant provides evidence that the divorce/annulment proceedings have commenced, and are likely to take a lengthy period of time to conclude.