REST api, POST entity with relationships?

I would suggest something like this.

POST /musicstore/artist/343/albums

{
    "Name":"AlbumName",
    "Description":"Some description for the album",
    "ReleaseYear": "1992",
}

The act of creating a resource as a child of the collection of albums for the artist 343 implicitly creates the relationship between the artist and the album. There is no need to specify it in the payload.