Older Quaker new tricks?

With time, patience and effort, you have a good chance of accomplishing what you want to do. Four isn't old for a QP, and parrots are capable of learning new things well into old age. You'd need to begin by making the parrot comfortable with you before attempting to hand tame her and to become less fearful of people. Once that's been accomplished, you'd be able to work on hand taming.