I think that this is your situation:
An artist can show their work at more than one gallery. A gallery can show the work of more than one artist.
If that is the case, you have a many to many relationship.
Start with these relationships:
Artists::__pkArtistID = Artist_Gallery::_fkArtistID
Galleries::__pkGalleryID = Artist_Gallery::_fkGalleryID
For an explanation of the notation that I am using, see the first post of: Common Forum Relationship and Field Notations Explained
You can place a portal to Artist_Gallery on the Artists layout to list and select Galleries records for each given Artists record. Fields from Galleries can be included in the Portal to show additional info about each selected Galleries record and the _fkGalleryID field can be set up with a value list for selecting Galleries records by their ID field.
In similar fashion, a portal to Artist_Gallery can be placed on the Galleries layout to list all artists showing work at that gallery.