Who is next in line for the throne Prince Harry or princess anne?

It is possible but highly unlikely. She is 10th in line to the throne, and will be pushed back further if any of her siblings or their offspring have any more children. Something would have to happen to make all of those unable to take the throne.

(There have been some changes proposed and agreed on, to change the rules of succession. One is to end male preference primogeniture, which meant a younger son would supplant an older daughter on the line of succession. However even when the change is fully enacted, it will not be retroactive, Anne will not move ahead of her three younger brothers.)