The writer of Hebrews used Psalms (and other Old Testament writings to show that Jesus is the FINAL fulfillment as the Son of God and Messiah. (Beyond David.) Some examples:
Ps. 2:7 - Hebrews 1:5 (“You are my son..”)
Ps. 8:4-6 - Hebrews 2:6-8(“You made him for a little while lower than the angels
Ps. 45:7-8 -Hebrews 1:8-9(“your kingdom...God anointed you...”)
Ps. 110:1- Hebrews 1:13 (“Sit at my right hand....”)
See the below link for further parallels between the Psalms and the New Testament.
http://www.jesuswalk.com/psalms/psalms-NT-quotations.htm
Catholic Doctrine Bible Study