Throughout this verse, David was acutely aware of the presence of the Lord. The Lord was with him even in the valley of the shadow of death. Sin, however, had weakened David's faith in the Lord's presence, so he begged the Lord not to cast him away. In addition, David requested that the Lord not remove His Holy Spirit from him.
This was a prayer that David had to pray. This was because the indwelling ministry of the Holy Spirit was limited to certain people in Israel at certain times prior to the Cross. The Spirit would indwell kings, prophets, and selected individuals for a specific ministry. However, it would leave when their task was completed or if they had sinned as King Saul did. However, this is entirely different from the permanent indwelling ministry of the Holy Spirit in the lives of all believers.
We can find comfort and encouragement in the psalms, prayers, and praises of David. Yet, we must never confuse God's dealings with His chosen people, Israel, before and after the Cross. For now, God is working through His Body, the Church. And one of the many blessings He has given to all believers is the permanent, indwelling Holy Spirit for all eternity and all time.

Dear Heavenly Father, I thank You for sending me a permanent, indwelling Holy Spirit to guide and lead me. There are times when I still have difficulty accepting Your forgiveness. It is not my desire to grieve or quench the Spirit due to unbelief or pride of life. Please help me to understand the vast, long, high, and deep extent of Your love. Let me be open to Your Word as I read it. May I learn how to apply Your wisdom to my life, and to understand Your direction. In Jesus's name I pray. Amen.