Q:

What do Time Lords typically use to explore space time?

Please correct me if I flub the details here, but I think it was in the Neil Gaiman episode The Doctor's Companion where the Tardis becomes a woman. We find out that the Doctor actually stole her from a museum because he thought she was so beautiful even if hopelessly outdated.
This begs the question: if by that point Time Lords no longer used Tardis's to travel through space and time, what method or technology did they use? Or did they simply no longer do so, since they had devolved into a decadent society where they looked down on anything so menial as actually traveling to lord over the time they claimed lordship over? I get the feeling it was more the latter, but I'm curious if we actually know? 
Please note that in well aware of how much the history has changed over the decades. Since this was a story told in the modern who-verse, I'm primarily interested in answers from the modern who-verse.

A:

The other Time Lords did use TARDISes. The Doctor's TARDIS is just a very old model.
The series 9 finale Hell Bent shows that the Time Lords still have a number of perfectly functional TARDISes lying around on Gallifrey, since a large chunk of it is about the Doctor and Clara stealing one.

DOCTOR: I had a duty of care. Listen, I'm nearly through here. (burble, clang) If I'm right, there should be a service duct under here. We'll be able to get to the old workshops. They'll have Tardises there. 

While we haven't seen any non-renegade Time Lords using them in a long time (I believe it hasn't happened once in New Who), this is probably because they're all hiding on Gallifrey, so there's currently no reason to believe they're using some other device to travel around. This was also re-confirmed in Hell Bent:

CLARA: You're monsters. Here you are, hiding away at the end of Time. Do you even know why? Because you are hated. You are hated by everybody. But by nobody more than me. 

The outdated status of the Doctor's TARDIS was known at least as far back as the 4th Doctor serial The Deadly Assassin, which provides us with this dialogue:

HILDRED: It looks
  SPANDRELL: Yes?
  HILDRED: If I didn't know better, Castellan, I'd swear it was a Type Forty.
  SPANDRELL: It is.
  HILDRED: But that's impossible.
  ...
  SPANDRELL: Data retrieval. Request information on all Type Forty TT capsules currently operational.
  COMPUTER: Negative information. Type Forty TT capsules are deregistered and non-operational.
  ...
  GOTH: Very well, Spandrell. I should like to see this Tardis. Extraordinary to think an old Type Forty is still operational.  

