Psalm 101:1 speaks of singing of mercy and judgment, which is echoed in Ephesians 5:19 where believers are encouraged to sing psalms and hymns, focusing on God's attributes.
Psalm 101:3's commitment to setting no wicked thing before the eyes is paralleled by Philippians 4:8's exhortation to think on things that are true, noble, and pure.
Psalm 101:6 speaks of God's favor towards the faithful, which is similar to 2 Chronicles 16:9 where the Lord's eyes search for those whose hearts are fully committed to Him.