I'm going to assume Paul's edit to the question is an accurate representation of daniel's intent, as he has made it just specific enough that I can now go into a decent amount of detail.
The Doctor is the only Time Lord going out of his way to help people all across the universe for most of the show's run.
There's a lot of ground to cover here, so first I'm going to address "the Time Lords" as a cohesive group and ignore the handful of "rogue"/"renegade" Time Lords off doing their own thing. And I'm going to start with New Who because, let's face it, that's the part most people reading this are going to be interested in.
In New Who, most of the Time Lords didn't exist, and then they were evil, and now they're in hiding. So they've never been a force for good the way the Doctor tries to be.
For the first few seasons of New Who, the Doctor was the only Time Lord left in the universe, so he was special for that reason alone.
Then in The End of Time we learn that the events of The Last Great Time War changed the Time Lords for the worse.
WILF: But you said your people were dead. Past tense.
DOCTOR: Inside the Time War. And the whole War was Timelocked. Like, sealed inside a bubble. It's not a bubble but just think of a bubble. Nothing can get in or get out of the Timelock. Don't you see? Nothing can get in or get out, except something that was already there.
WILF: The signal. Since he was a kid.
DOCTOR: If they can follow the signal, they can escape before they die.
WILF: Well, then, big reunion. We'll have a party.
DOCTOR: There will be no party.
WILF: But I've heard you talk about your people like they're wonderful.
DOCTOR: That's how I choose to remember them, the Time Lords of old. But then they went to war. An endless war, and it changed them right to the core. You've seen my enemies, Wilf. The Time Lords are more dangerous than any of them.
Note that later in that episode we found out the Time Lords were literally trying to bring an end to all of time and space.
This appears to have changed when the Doctor found a way to retroactively save Gallifrey from the Time War in The Day of the Doctor by placing the planet in a pocket universe. In the next episode, The Time of the Doctor, we discover the Time Lords are asking (in a suitably convoluted and timey-wimey way) whether or not it's safe to return to their home universe, and the Doctor doesn't answer them because it's not safe.
It's been explicitly confirmed as recently as Hell Bent that Gallifrey is still in hiding, and still has a pretty bad reputation:
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.
So that's probably not going to change for a while.
In Old Who, the Time Lords were very non-interventionist. In fact, it seems like the only times they did go out of their way to help the universe at large were when the Doctor asked them to.
This is established in the very same story that first introduced the Time Lords: The War Games.
ZOE: What did he mean, Doctor? Who mustn't you call?
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.
DOCTOR: The Time Lords holding a trial is a very rare event.
DOCTOR: Well, normally they don't interfere with the affairs of other planets, but they had to when I called for help.
TIME LORD: You have heard the charge against you, that you have repeatedly broken our most important law of non-interference in the affairs of other planets. What have you to say? Do you admit these actions?
DOCTOR: I not only admit them, I am proud of them. While you have been content merely to observe the evil in the galaxy, I have been fighting against it.
TIME LORD 3: It is not we who is on trial here, Doctor, it is you.
DOCTOR: No, no, of course, you're above criticism, aren't you.
TIME LORD: Do you admit that these actions were justified?
DOCTOR: Yes, of course, I do. Give me a thought channel and I'll show you some of the evils I've been fighting against.
[the Doctor shows them the many monsters he fought during the first few seasons of Doctor Who]
DOCTOR: All these evils I have fought while you have done nothing but observe. True, I am guilty of interference, just as you are guilty of failing to use your great powers to help those in need!
TIME LORD: Is that all you have to say?
DOCTOR: Well, isn't it enough?
The Third Doctor also tells a story that confirms this is not the first time he's tried (much less succeeded) in talking the Time Lords into doing something.
DOCTOR: We are to those creatures up there, Jo. Roll up! Roll up! Roll up! And see these funny little creatures in their native habitat! Watch them go through their funny little tricks! Poke them with a stick and make them jump!
JO: Oh, stop it, Doctor. It's not funny.
DOCTOR: No. Oh no, believe me, I'm just as angry as you are. As a matter of fact, I had a great deal to do with the banning of these miniscopes.
JO: You did?
DOCTOR: Yes, I did. I managed to persuade the High Council of the Time Lords they were an offence against the dignity of sentient lifeforms.
JO: But I thought the Time Lords never interfered?
DOCTOR: Yes, well, they don't as a rule. But, frankly, I made such a nuisance of myself. Well, they banned the things.
All of the other characters who could be considered renegade Time Lords are either evil, trying to keep a low profile, or in another universe.
The Master, Omega, The Rani and The Monk are not exactly upstanding citizens when they appear in the TV show. When they interfere with the rest of the universe, they do so for their own selfish reasons.
At first, Romana was babysitting the Doctor for the High Council of Gallifrey. After many seasons together, she eventually came around to the Doctor's way of looking at things, and in her final TV story (Warrior's Gate) decided to stay in E-space (aka, another universe) to help the Tharils.
If we count unaired episodes, then it's worth noting Doctor Chronotis from Shada is simply trying to keep a low profile on Earth, since he's actually one of Gallifrey's most notorious criminals.
The Meta-Crisis Doctor is trapped in another universe.
Donna was sort of a Time Lord for a brief while, but the Doctor had to undo that to keep her from dying.