Yes, you can get a legal grant to cross over someone else’s land. Although most people have a right to their private property, there are certain legally-protected exceptions. These are called easements.
An easement is an official right that you might have to cross or use another person’s property for a specific purpose. There are four types of easements: utility easements, private easements, easements by necessity, and prescriptive easements. All four varieties are iron-clad and do not go away when the property changes hands. If you had one when your old neighbor was there, then you still have it.
If you do have an easement, it’s probably mentioned on your new neighbor’s deed. You can ask her if she’s willing to look over the relevant documents with you to see if an easement is mentioned. If she refuses, you may need to take legal action to protect your rights. Hopefully, though, you two can resolve things amicably.