Is it expected to give a gift to a First Holy Communion when not attending?

This would depend on local custom, your relation to the communicant or communicant's family and whether you were invited and had to decline for whatever circumstances. First Communions can sometimes be gaudy affairs when it comes to gifts, which is unfortunate. Appropriate gifts you cannot go wrong with might include a rosary, a holy medal with the communicant's patron saint on it, or a book of their patron saint. Often, gift-giving at religious occasions has become a social event and so you should gauge whether the family is expecting a gift as it is not strictly necessary from a religious stand point unless you are a godparent or perhaps a direct relation.