Can be tamed.
Located in Springrain River, The Emerald Dream. Astera initially appears as an untameable dream bear and turning her into a tameable thornbear requires a small adventure. Firstly, obtain a Thorn-Laden Heart, which has a low chance of dropping from bears in the Emerald Dream zone in the Dragon Isles (this heart will mention 'bear' in its description - there are also stag and saber versions, but they're for taming other thornbeasts). Once you have the heart, proceed to Drustvar in Kul Tiras and visit Athainne who is sometimes found in Ulfar's Den in the mountains far south-west of Fallhaven (approx. 46,45), and sometimes she wanders along the river below the den (around 52,40) with Athair. If she's not present in either location then you may have to wait - her schedule is unpredictable and it's also possible she disappears completely during daylight hours. Present the heart to her and she'll give you some Moontouched Thorns. Then speak to Ulfar, select his 'I have seen some animals...' dialog, then the dialog about Athainne, and he'll give you a Thornspeaker Ritual Knife. With the knife, proceed to the banks of the Springrain River, west of Amirdrassil in the Emerald Dream and look for a dreambear named Displaced Bristlebruin. She should be sleeping on some grass on the south bank of the river at 37,62 (near a cave with a pair of Invasive Podlings). Her colour will determine which thornbear you'll end up with: if she's initially a dark brown dream bear she'll turn into a dark thornbear, golden brown becomes brown, and green & brown becomes green, so you may need to kill and reset her if she's not currently in the colour you need. After you kill her as a bear, use the ritual knife on her corpse and she'll resurrect as a thornbear which you can tame!