The passage is actually Psalms 138, not 137. Here is a summary:
David expresses his gratitude to God, promising to worship and praise Him in the presence of angels, and he asks God to hear his prayers and multiply virtue in his soul. David also expresses his desire for all the kings of the earth to acknowledge and praise God. He acknowledges God's greatness and His favor towards the humble, and he expresses his trust in God's ability to deliver him from tribulation and his enemies.
1 Of David himself. O Lord, I will confess to you with my whole heart, for you have heard the words of my mouth. I will sing psalms to you in the sight of the Angels 2 I will adore before your holy temple, and I will confess your name: it is above your mercy and your truth. For you have magnified your holy name above all 3 On whatever day that I will call upon you: hear me. You will multiply virtue in my soul 4 May all the kings of the earth confess to you, O Lord. For they have heard all the words of your mouth 5 And let them sing in accordance with the ways of the Lord. For great is the glory of the Lord 6 For the Lord is exalted, and he looks with favor on the humble. But the lofty he knows from a distance 7 If I wander into the midst of tribulation, you will revive me. For you extended your hand against the wrath of my enemies. And your right hand has accomplished my salvation 8 The Lord will provide retribution on my behalf. O Lord, your mercy is forever. Do not disdain the works of your hands