House of the Dragon season 3 split up its biggest dragon from her rider way back at the beginning of the season. Nearly three-quarters of the way through the season, we still haven't seen Aemond and Vhagar reunite, despite his intentions to find her in season 3 episode 6.
After leaving King's Landing at the request of his mother, Aemond and Vhagar flew to Harrenhal, killed the remaining Strong family members, and took the castle. Aemond also suffered a serious injury, and he was rescued by the alleged witch, Alys Rivers.
Alys nurses Aemond back to health, but everyone is left asking the same question: Where is Vhagar?
Aemond makes several attempts to leave Harrenhal to find his dragon in the latest episode, but he's unsuccessful in actually starting his search for his dragon.
So, where is she and why dd he leave? I've picked the three most likely scenarios about Vhagar's absence and her reasons for leaving Aemond behind in Alys' care.

Vhagar is just a dragon being a dragon, and she’s hungryÂ
I think it's much more likely that Vhagar is just doing her thing. Like, she's been riderless before, of course, but she's also been apart from Aemond for extended periods of time after they bonded. To me, the most likely answer is simply that Vhagar is a dragon, and dragons get hungry
Vhagar was spotted near Wendish Town in the previous episode, and as I recall, she burned the town and probably ate some livestock or people. We saw Baela and Addam of Hull on the lookout for Vhagar, but they were unable to find her.Â
When Aemond didn't return after going into Harrenhal, perhaps, Vhagar just left to go grab a snack.

Alys performed some kind of witchcraft to interfere with Aemond and Vhagar's bond
There are many, many theories about why Vhagar left Aemond. I've delved deep into the Aemond-Alys lore, and there is a not-so-small group who believe that Alys is literally working her magic on Aemond or Vhagar to keep them apart.
I don't know what specific kind of magic that could be, but it's definitely possible that Alys is doing something to Aemond, just like she did to Daemon in House of the Dragon season 2. Remember, Helaena mentions that "he burns, but without fire." His sister has powers of her own. She is a dreamer, though not the only one.
There's definitely something wrong going on here with Helaena, Alys, and Aemond. I don't know specifically what Alys could do to block a bond with a dragon and prevent Aemond and Vhagar from being together, but it feels like there's always magic in the air at Harrenhal. Is it real? That's my big question.
Do I actually believe that Alys is using her powers to block Vhagar and Aemond's bond? Not really! I think Alys actually reveals the answer in season 3 episode 6.

Vhagar is protecting Aemond by leaving Harrenhal
Look, I don't know how much dragons actually know about this conflict or what is happening politically. Does Vhagar know that Rhaenyra has a bounty on their head and everyone in the Seven Kingdoms is trying to kill them? I'm not sure.
But, if she did, it would be very stupid for Vhagar to stay in Harrenhal waiting for Aemond to come out. She would be a sitting duck outside the castle for any and all enemy dragons to swoop in and attack her while she chilled outside the castle waiting for Aemond to come back. There’s reason to believe she left Aemond so keep him out of danger.
I think this is the theory that I would most like to believe. I can't explain how Vhagar would know, but it makes sense in a way that Vhagar would drop Aemond off and leave when he didn't return, to keep herself safe and to keep Aemond safe. If she has a sense of the danger that they are in, and she likely does after being alive for as long as she has, Vhagar could basically hide out for the time being, lay low, and wait for Aemond to emerge.
This isn't the most likely theory, but I think dragons in this show are way smarter than we give them credit for. Without Aemond, Vhagar knows how to survive and thrive on her own. That's probably what she's doing, while hoping her rider, the human she has the bond with, will be all right in time.
If not that, she's probably just hungry.
Hopefully, we don't have to go much longer before Vhagar returns and finds Aemond, but there are only two episodes of House of the Dragon remaining this season after episode 6.
