This is another question about the Holy Spirit which has recently been posed to me.  Once again, I am reluctant to discuss such a ‘shy sovereign’, who is more to be experienced than analysed.  Nevertheless, I offer a few thoughts:-

The Bible does teach a certain order in the operations and activities of the members of the Trinity. For example, according to Jn 14:26, the Holy Spirit is sent by the Father in the name of the Son.

The usual norm is to address pray to the Father, as Jesus both practiced and taught.

Occasionally, it seems that the risen and exalted Christ was addressed in prayer, 2 Cor 12:8-10.

The Holy Spirit is never directly addressed in Scripture. He has no proper name. He points away from himself, to Jesus. We do not pray to him; he prays for us, Rom 8:26f.

Nevertheless, ‘prayer to the Spirit will be proper when what we seek from him is closer communion with Jesus and fuller Jesuslikeness in our lives.’ (Packer, Keep in Step with the Spirit, 261.

B.M. Palmer, in his great work on the Theology of Prayer, puts it thus:-

Prayer may undoubtedly be offered to each of the Three Persons, for two substantial reasons: The first is, that however they may be discriminated, they cannot be separated one from the other. The three do not make one God, as by composition; they are the one God, through the indivisible essence or being which is the equal property of each. If, therefore, divine in the supreme sense, each Person may equally be the immediate obejct of address, though not the exclusion of the others…The second reason is, that in the functions which they discharge, each is supreme in his own work, and must stand in immediate relation to the creature who is to be saved…It would seem fit, therefore, that each may be immediately addressed in all that concerns his specific work. The natural mode of communication, however, would be to the Father, through the Son and by the Spirit; these prepositions simply indicating the co-ordination of the parties to the covenant, and of their several offices. (199f)

In fact, many of the classic hymns about the Holy Spirit are addressed to him:-

‘Veni Creator Spiritus’ (‘Come, Holy Spirit’)
‘Come down, O Love Divine’
‘Spirit of wisdom, turn our eyes’
‘Holy Spirit, hear us’
‘O breath of God, breath on us now’
‘Holy Spirit, truth divine’
‘Spirit divine, attend our prayers’
‘Come, Holy Ghost, our hearts inspire.’
‘Come, Holy Spirit, come!’
‘Breath on me, Breath of God’