Why isn’t Communion, the Eucharist or the Lord’s Supper, mentioned in the creeds of the church?
This could be a very short answer, but I will do my best to string it out a bit.
The Nicene Creed came about in 325AD and it was essentially a way to combat Gnosticism and the Arian controversy. Building on this creed, other creeds came along from different counsels, 381 Constantinople, 451 Chalcedon. The creed(s) were essentially baptism confessions of faith and they were intended to show right belief before baptism. This is why the creeds were packed with as many tenants of the faith as possible in the smallest space.
They were not intended to be an exhaustive exposition of every aspect of the faith and life in the family of Christ.
The church, for a very long time, also would not let anyone partake in communion until they were baptized as a confession of faith. This also shows why communion is not mentioned in the creeds because it came after baptism.
Today there are some churches who will recite the Nicene creed before communion, as part of the confession.