Someone who is interested in the languages created by Tolkien for his Middle-earth races, usually Elvish (Quenya and Sindarin).
There are many categories of linguists:
some are romantically interested in learning Elvish so that they can talk it fluently or write poems, and possibly understand and 'touch' the beauty of the Elves.
Others on the other hand are not so romantic and aren't interested in Elves more than they are interested in Númenoreans. They study the languages so that they will understand Tolkien's linguistic mind and system, find out what real languages were his insipiration, and possibly understand other real langauges better. They know that Elvish (and Tolkien's other languages) are not that much developped so that they can use them.
Because Elvish aren't much developed, some like to construct new words, more or less like Tolkien did, based on the Elvish etymology system. Others are more purist and consider it a desecratoin: the result is not Tolkien's Elvish but neo-Elvish.