I will shout for joy as I play for you; with my whole being I will sing because you have saved me.” (Psalm 71:23, GNB)

In the Good News Bible, while the author is not mentioned, the title they have given to this psalm is The Old Man’s Prayer.  Certainly the psalmist appears to be looking back on a long life and how God has been faithful:

I have relied on you all my life; you have protected me since the day I was born. I will always praise you.” (Psalm 71:6, GNB)

He also calls for God to continue to be his God in his old age:

Do not reject me now that I am old; do not abandon me now that I am feeble.” (Psalm 71:9, GNB)

Now that I am old and my hair is grey, do not abandon me, O God! Be with me while I proclaim your power and might to all generations to come.” (Psalm 71:18, GNB)

The context of our verse is that the psalmist (David?) vows that he will play his harp for the Lord, he will sing with his whole being as he plays because he understands that God has saved him.  The psalmist looks back on a life of deliverance and it causes him to sing with all his might and strength, to sing so vibrantly that it affects his whole body.  He has seen God’s salvation in his life and he will continue to see it in old age.

Spurgeon comments here:

Soul singing is the soul of singing. Till men are redeemed, they are like instruments out of tune; but when once the precious blood has set them at liberty, then are they fitted to magnify the Lord who bought them. Our being bought with a price is a more than sufficient reason for our dedicating ourselves to the earnest worship of God our Saviour.