Time Lords have possessed psychic ability as demonstrated going all the way back to the 2nd Doctor, Patrick Troughton, when in "The War Games", The Doctor sent an emergency message* to Gallifrey upon discovering the true nature of the Games.
DOCTOR: The only people who can put an end to this whole ghastly business and send everyone back to their own times. The Time Lords.
JAMIE: Who are they?
DOCTOR: They're my own people, Jamie.
JAMIE: Oh, well, that's all right, then.
ZOE: But it isn't all right, is it, Doctor.
DOCTOR: No, it's not, Zoe. But I'm afraid that there's no alternative.
(The Doctor sits on the floor and puts six plastic squares in a circle in front of him. Then he closes his eyes and concentrates.)
JAMIE: What's he doing?
WAR CHIEF: Don't do it, Doctor. You can't! You know what will happen!
(The squares form themselves into a cube.)
JAMIE: Look at that!
JAMIE: Doctor, what's that?
DOCTOR: It's a very special sort of box. It now contains all the information about what's been going on here, and an appeal for help.
JAMIE: Help? Who from?
ZOE: The Time Lords?
DOCTOR: Yes, Zoe.
The psychic ability of the Doctor (and presumably other Time Lords) is demonstrated several times over the course of the following Doctors (sadly more than I can recall off hand). At one point the 4th Doctor receives a psychic message from Gallifrey calling him home.
SARAH: Oh, and boy am I sick of that sonic screwdriver! I'm going to pack my goodies and I'm going home. I said, I'm going to pack my goodies and I am going home! Right! Excuse me!
(Sarah storms out of the console room.)
DOCTOR: What was that you? I don't know why she goes on like this. There's really nothing the matter at all.
(The Doctor gets a mental wave.)
DOCTOR: The call. The call from Gallifrey. Gallifrey. After all this time, Gallifrey. I can't take Sarah to Gallifrey. Must get her back home. Must reset the coordinates. South Croydon
*This emergency message system is re-introduced in "The Doctor's Wife" when the white flying cube knocks on the TARDIS door.
(The Doctor opens the doors. A small glowing box is outside.)
DOCTOR: Oh, come here. Come here, you scrumptious little beauty.
(The box flies inside and ends up hitting the Doctor on the chest.)
RORY: A box?
AMY: Doctor, what is it?
DOCTOR: I've got mail. Time Lord emergency messaging system. In an emergency, we'd wrap up thoughts in psychic containers and send them through time and space. Anyway, there's a living Time Lord still out there, and it's one of the good ones.