…A communion service is held when a priest is not available. …
No, a priest can preside at a communion service. This is what happens on Good Friday. There is not a Mass, there is no Eucharistic Prayer, no consecration, no turning of bread and wine into the Body and Blood of Christ.
The priest is limited in how many times he can celebrate Mass in one day. But there is no limit to how many times he presides at a Communion Service.
The 1973 liturgical book “Holy Communion and the Worship of the Eucharist Outside of Mass” has:
“14. The faithfuly are to be led to the practice of receiving communion during the actual eucharistic celebration.
Priests, however, are not to refuse to give communion to the faithful who for a legitimate reason ask for it even outside Mass.”
(The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 643).
The 1983 Code of Canon Law also has this:
“Can. 918 It is most strongly recommended that the faithful receive holy communion in the course of a eucharistic celebration. If, however, for good reason they ask for it apart from the Mass, it is to be adminstered to them, observing the liturgical rites.”
(The Code of Canon Law: New revised English Translation, HarperCollins Liturgical, 1997, ISBN 000599375X.).