Many young Catholics do not realize that the Church has long honoured those in the Old Testament who were given grace. Unlike us in baptism, which is available to all, some had grace in the ancient times. St. David is considered the person most after the heart of God in the Old Testament.
Here is what Luke writes in Acts 13:22, quoting
And when he had removed him, he raised them up David to be king: to whom giving testimony, he said: I have found David, the son of Jesse, a man according to my own heart, who shall do all my wills. DR
God tells Samuel that David is a man who loves and will obey Him. Here are some cross references which push the point. Saul had a disobedient will, but David, although he sinned, did repent and loved God. That is the key; he loved God passionately. This is clear in the Psalms.
1 Samuel 16:13 So Samuel took the horn of oil and anointed him in the presence of his brothers, and from that day on the Spirit of the LORD came upon David in power. Samuel then went to Ramah.
Psalm 89:20 I have found David my servant; with my sacred oil I have anointed him.
Acts 7:46 who enjoyed God's favor and asked that he might provide a dwelling place for the God of Jacob.
Acts 13:36 "For when David had served God's purpose in his own generation, he fell asleep; he was buried with his fathers and his body decayed.
Also, David is a type of Christ. He is priest, king, prophet. He is promised that the Messiah and the greatest king of all would come from his line, and this is Christ, of the House of David.
Indeed, we should honour St. David. The Medievals obviously did.