Horselvr, Confirmation is not necessary to receive Communion in the Catholic Church. If that were so, all of our 7 and 8 year old First Communicants would not be able to receive the Sacrament! An adult who has received their Baptism and First Communion but has not been Confirmed (and there are plenty of those) only needs to go to Confession and be free of mortal sin. Of course, they should seek Confirmation as soon as possible. We do not require our adult RCIA candidates who have been previously Baptized in the Catholic Church and Communed to refrain from Communion until they have been Confirmed. The only really necessary Sacrament is Baptism, and Confession if one is in mortal sin. However, all Catholics should be Confirmed, it is a very important Sacrament.
A person, however, who has been baptized but never catechized, should receive catechesis first, then Confession , Communion and Confirmation, mostly this is done through RCIA. However, strictly speaking, the Confirmation is not required. My husband was received into the Church and Baptized as an adult, but never did get Confirmed–although I frequently encourage him-and it is permissible for him to receive Communion. We also got married without him being confirmed, as that is not strictly necessary, although it is highly encouraged these days.
I am only pointing this out because there may be baptized Catholics out there coming back to the Church, who have received their First Communion who may think that they have to wait until they are confirmed, when that is not so. They can return and go to Confession and Communion and then seek Confirmation. However, they should speak with their parish priest and follow his instructions on the matter.