This may also include the burning of other blessed things such as linens or vestments…old Bibles…prayerbooks…etc that have become too worn to be reverently used.
This service is designed for Shrove Tuesday (perhaps in conjunction with a Pancake Feast).
To “bury” the ALLELUIA a suitable banner might be assembled and a processions made, with it, to the place of the palm burning. Traditionally this was done on Septuagesima to recall the years of captivity in Babylon where the Lord’s people said, “how can we sing the Lord’s song in a strange land?” (Ps 137)

Presider: In the Name of the Father, and of the Son and of the Holy Spirit. ALL: Amen

Presider: We gather here to turn these palms from last year’s celebration of Palm Sunday into ashes (along with other blessed things that have become too worn to be reverently used). We also bury the Alleluia, the “Lord’s Song” as we prepare to enter the holy Season of Lent.

As the fire gets going, those present can carefully add palms, etc to keep it burning.
As the fire is tended, the procession moves to “bury” the ALLELUIA….perhaps folding the banner and tucking it into a chest or such action until its reappearance at Easter!
During the procession this hymn might be sung…or other deemed appropriate:

ALLELUIA, SONG OF SWEETNESS (Hyfrydol or other 8787D tune)
Alleluia, song of sweetness, Voice of joy that cannot die; Alleluia is the anthem Ever raised by choirs on high; In the house of God abiding Thus they sing eternally.
Alleluia thou resoundest, True Jerusalem and free; Alleluia, joyful mother, All thy children sing with thee; But by Babylon’s sad waters Mourning exiles now are we.
Alleluia cannot always Be our song while here below; Alleluia our transgressions Make us for awhile forgo; For the solemn time is coming When our tears for sin must flow.
Therefore in our hymns we pray thee,
Grant us, blessed Trinity, At the last to keep thine Easter, In our home beyond the sky, There to thee for ever singing Alleluia joyfully.

Returning to the fire, the following prayer is offered:

The Lord be with you. And also with you. Let us pray. Living God, in their life these palms drew life from the earth and gave it back to our air and the animals they hosted and sheltered; in the worship of our community, they helped us offer festive joy: Grant now, O God, that these palms, reduced to ashes, may be for us a sign of your power to purify our hearts. May we recognize your love at work in us, replanting our lives in the sure and humble soil of your truth and grace. Through Jesus Christ our Lord, who lives and reigns with you and the Holy Spirit, One God, now and forever. Amen.

A Blessing or the Grace brings the service to a close.

The following is a good Ash Wednesday Hymn linking the palm burning to the day:

SUNDAY’S PALMS are WEDNESDAY’S ASHES Sunday’s palms are Wednesday’s ashes as another Lent begins; thus we kneel before our Maker in contrition for our sins. We have marred baptismal pledges, in rebellion gone astray; now, returning, seek forgiveness; grant us pardon, God, this day!
We have failed to love our neighbours, their offenses to forgive, have not listened to their troubles, nor have cared just how they live, we are jealous, proud, impatient, loving overmuch our things; may the yielding of our failings
be our Lenten offerings.
We are hasty to judge others, blind to proof of human need; and our lack of understanding demonstrates our inner greed; we have wasted earth’s resources; want and suffering we’ve ignored; come and cleanse us, then restore us; make new hearts within us, Lord!