The new series has established that Timelords have a psychic link to one another that means that they can detect each other. Obviously this is a ret-con of RTD's and didn't exist in the original series run.

As we've seen in The Time Meddler and Planet of the Spiders thr Doctor failed to recognize both the Monk and K’anpo Rinpoche/Cho-Je as Timelords.

Now K’anpo Rinpoche is a contemporary of the Doctors, but the Meddling Monk isn't, he left Gallifrey some 50 or so years after the Doctor, so technically they are out of phase with one another.

Timelords from different time periods might not have the same psychic link, hence why the Doctor didn't recognize The Monk as being of the same race as him on their first encounter.

The Monk don't seem the type to jump at the chance at front line service during the time war, it could be argued that he, and others like him are knocking around someplace in time and space, all out of phase with the Doctors psychic link and undetectable to him.

The whole concept of this is fascinating. In "The Deadly Assassin", the Doctor was recognised, but with the caveat, "Have you had a facelift?" Not necessarily implying psychic link, though, simply that the two Time Lords had history.

And, as with the Master, anything has become possible with the introduction of the Chameleon Arch!

Rumours abound about the Monk... Patrick Stewart's name is constantly linked with the role. Who knows?