Is there a "definitive" database for Mobile Genetic Elements?
Would advise doing Denovo identification method structure-based. Then use these public databases (  RepBase, Dfam ) to look for high similarity or homology exploration, this possibility if your species, the repeats not yet discovered, or deposited in the databases.

If the species well-investigated earlier and the mobile element recognised, I assume it will be a straightforward task using species-specific search via Repeatmasker tool with the -species flag to obtain the MobileElement annotation in the genome.

Let me know if you need any data from Repbase related to your species, i have an entree.