And those who know Your name put their trust in You,For You, O YHWH, have not forsaken those who seek You.
Much of the OT poetry is written in couplets, two lines that are getting across one primary point. These can also be called "parallelisms."
I love the parallel we are confronted with in Ps 9.10. It shows that trusting God and seeking God are intertwined realities. There is always an initial saving arrival at belief or trust in God in the broad theological sense, but here David is delighting in the ongoing pursuit of God as trust. The righteous kingship of YHWH in Ps 9.1-12 is grounds for David's believing and pursuing.