SOLVED: How can I add a bone constraint to an already animated bone without affecting the animation?

Question

Sorry I realise the title is not as clear as I'd like but I could not think of a better one!

I have animated a hand and fingers to play a bass guitar using Auto-rig Pro. While not perfect, the animation is a decent attempt to accurately represent the playing of a specific bass-line.

After completing this, I realised that I'd also like the player and instrument to move a little. However, the animation was done with the neck of the bass in a specific location with a specific rotation. If the bass moves the animation of the hand will lose its accuracy.

So I'd like to put a constraint on the hand to move its location and rotation relative to the neck of the bass while not interfering with the movement up and down the neck from the animation.

Edit:

1. As suggested by Chris, I have now uploaded a .blend file to Blend-Exchange:
2. Also the following two images demonstrate the problem:

1. The bass has been parented to the player's root.x bone

2. As the player's hips are moved, the bass moves away from the fingers.

As always, any pointers or suggestions are as welcome as a full answer.

Answer 1

This turned out to be surprisingly easy. I just added a second Child Of bone constraint for the hand controller, above the one that had been created automatically by Auto-rig Pro, and used the instrument as the target.

Here you can see the position of the hand at frame 835.

Here, the player and instrument have moved; the hand keeps its position relative to the instrument while continuing to follow the original animation.