Whenever Scripture mentions the three persons of the Trinity together, the purpose is to say something about our Christian lives and the importance of our relationship with each of the Divine Persons for our spiritual life. Thus Jude encourages us: "Praying in the Holy Spirit, persevere in God's love, and welcome the mercy of our Lord Jesus Christ which leads to life eternal."
"Praying in the Holy Spirit" is an idea that occurs throughout the New Testament, though with slightly different words. St John records that Jesus said true worshippers of the Father are those who worship in Spirit and Truth (Jn 4:24), where he obviously means "the Spirit of Truth" (cf. Jn 14:17). When we are born again through water and the Spirit, the Holy Spirit makes us new creatures, children of God the Father: we must live in grace and persevere in the love of God.
In Romans 8:26-27, St Paul movingly teaches us that the Spirit prays in us and for us when we do not know how to pray.
The mercy of our Lord Jesus Christ is manifest in the Trinity sending Jesus out of divine love in order to save us.
Holy Spirit, teach us to pray, to persevere in the love of the Father and so be nourished by the mercy of our Lord Jesus Christ.