I completed the Antiquarian tutorial quest, and recently dropped back by through Solitude to say hello to my favourite little nerdy mage, only to find that she's completely gone. This might not be a bug, since it doesn't necessarily impede progress or anything, perhaps it's more just like Hiranesse (from Summerset; just outside of Wasten Coraldale) where she's removed from the game after you complete her quest.
Although "story-wise", Gabrielle's disappearance doesn't make sense considering you can still get messages from her in the Circle when you dig up new antiquities.
TL;DR—where's my girl Gabrielle at? is it a bug or is her removal from Solitude after the Antiquity tutorial quest an intended feature?
Shortly after the formation of the Ebonheart Pact, a Nord woman was given a tour of the Tribunal Temple. When later asked about the experience, she seemed upset. Suffice to say, the Dunmer were not pleased to hear this, and thus they inquired further.
"Well," the Nord frowned, "the priests were very angry and unwelcoming. They kept shouting things at me like "you can't drink that mead in here!" and "somebody stop her, she's running naked!" and "we can't catch her; she's covered in grease!""