The Monk's TARDIS was a Mark IV TARDIS owned by the Meddling Monk.
History
The Monk's Tardis is Discovered - Doctor Who - The Time Meddler - BBC
Vicki and Steven discover the Monk's TARDIS. (TV: The Time Meddler)
Unlike the First Doctor's TARDIS, at this time the Monk's TARDIS had a functional chameleon circuit and directional unit. Its control console was also set on a dais, as opposed to being at floor level. After visiting several moments in Earth history, he landed in Northumbria in 1066 and disguised his ship as a Saxon altar in his monastery. The Doctor learned of the Monk's plans to change history and sabotaged his TARDIS, making it the same size inside as outside. This made it impossible for the Monk to get inside it. (TV: The Time Meddler)
The Monk eventually managed to fix the dimensional controls, re-creating the interior dimensions, and thus escape from 1066. On a later adventure on the volcano planet Tigus, Mortimus's ship turned into a large rock. Meeting again in ancient Egypt, the First Doctor changed it into a police box so Mavic Chen and the Daleks would mistake it for the Doctor's TARDIS. During the Doctor's reprogramming of the chameleon circuit of the Monk's TARDIS, the ship briefly took the forms of a motorbike, a Western covered wagon and a World War II tank. He also stole the Monk's directional unit so the Monk would re-materialise in a random location. The Monk ended up in an frigid planet with his TARDIS disguised as a block of ice. (TV: The Daleks' Master Plan)
When the Fifth Doctor next encountered the Monk, he appeared to have voluntarily re-configured his TARDIS into a police box. The Monk had the top of his ship's roof blown off by Ice Warriors with a sonic cannon. (COMIC: 4-Dimensional Vistas)
The Seventh Doctor met the Monk in London in 1976. Mortimus, posing as a record executive, had turned his ship into a desk, complete with scraps of paper. The papers retained some of the special qualities of his TARDIS, allowing the Doctor to use them to return to Earth after the Monk vengefully tried to abandon him on the same icy planet where he had been trapped. (PROSE: No Future)
The Eighth Doctor, along with his new companion Tamsin Drew, had a reunion with the Monk in the Abbey of Kells in Ireland in the year 1006. Under the alias of Abbot Thelonius, the Monk used the impressive artistic skills of the monks to draw a new directional circuit for his TARDIS, using a page of the Book of Kells and liquid Gallifrite. Unknown to the Monk, Tamsin had switched his circuit for a false one, prior to the first test of the circuit and again the Monk's TARDIS was crippled. However, the Monk was able to rectify this and had several more meetings with the Doctor. (AUDIO: The Book of Kells)
When the Monk took Tamsin Drew to the planet Halcyon in the 33rd century, his TARDIS assumed the form of a Punch and Judy tent. He told her that it could have taken the form of a tree which would have made it less conspicuous, but that would also have made it more difficult to find, given that it had materialised in a forest. (AUDIO: The Resurrection of Mars)