A hymn to complete another hymn, or a hymn to complete a section of worship, is how we might think of singing the Doxology, or the Gloria Patri. The Doxology known to most Protestants was composed by Thomas Ken in the 17th century, and a common version of the Gloria Patri was composed by Charles Meineke (1782-1850). This is the so-called Lesser Doxology, the Greater Doxology being the Gloria in Excelsis, still used in the Catholic Mass.
The idea behind doxologies comes from Scripture itself, where a section of Scripture is concluded with a doxology. Paul does this (Romans 11:36, Galatians 1:5, and Ephesians 3:21), and each of the five books of the Psalms ends with a doxology (Psa 41:13, 72:18-19, 89:52, 106:48, 150:1-6) The tradition of singing doxologies at the end of hymns goes back to the synagogue and ancient Christian worship.
Besides biblical and historical reasons, a church might consider using doxologies for some practical reasons. First, it roots us in a robust Trinitarian worship. Our worship should never be so generically monotheistic that its distinctive Trinitarian emphasis is lost. We worship the God who is Three. We address the Father, through the Son, by the Spirit. We honor Christ, who is the radiance of the Father, whom the Spirit testifies of. We praise the Spirit, who is the Lord, and whose fellowship enables us to know the Father’s love for the Son, and the Son’s love for the Father.
Second, the doxology promotes a healthy catholicity and sense of the call for universal worship. In singing the Doxology we call on creatures here below and the heavenly hosts above to worship with us. As hymns such as “All Hail the Power of Jesus’ Name’, “Holy God We Praise Thy Name”, and “All Creatures of Our God and King” do, the Doxology calls on more than simply our local congregation to praise God. It echoes Psalm 150- everything that breathes has an obligation to worship.
In some ways, these are extended “Amens”, and used well, unite a congregation in its commitment to the historic faith, and the obligation for all to worship the Triune God of that faith.