The Gestalt's timeship

Whoever was the current host of the Gestalt could use a timeship.

Its exterior was blue and rectangular, making it fairly conspicuous in most settings. The interior was a large, circular, candle-lit room whose walls resembled castle walls. There were bookcases on the far wall, two large couches and a central console. During Kady Williams's tenure as the Gestalt's host, the stone walls were adorned with pictures of people she had known throughout her travels, including Miaki, Lyth and Elya. (PROSE: Ring Theory)

Behind the scenes
The description of the timeship as blue and rectangular makes it resemble the Doctor's TARDIS, suggesting that the entity who became the Gestalt was actually a far-future version of the Doctor. However, for copyright reasons, this was obviously not made explicit.