Is possessive noun is a noun that is always plural elf?

No, possessive nouns can be singular or plural.

A possessive noun is used to show that something belongs to that noun.

The possessive form of the singular noun elf is elf's.

example: The elf's hat had a feather in the brim. (the hat of the elf)

The possessive form of the plural noun elves is elves'.

example: The elves' party was such fun. (the party of the elves)