E is for Engin

The above still frame comes the phenomenal story during the 4th Doctor's reign, The Deadly Assassin.

Apart from a few scenes in The War Games and The Three Doctors, Assassin is our first real glimpse at Time Lord society on Gallifrey. 

Above with Tom Baker, on the left is Castellan Spandrell (played brilliantly by George Pravda). A Castellan being much like a Chief of Police on Gallifrey.

On the right is Coordinator Engin (portrayed by Erik Chitty).

A rather overlooked underestimated Time Lord, this diminuitive and nervous man was actually the catalyst for one of the most important positions in the Time Lord hierarchy.

The Coordinator position was one that oversaw and guarded the entry points to the Time Lord Matrix, a vast surreal repository for the living minds of dead Time Lords.

Engin assisted the 4th Doctor in his ongoing feud with the Master, the battlefield now their home planet itself.  Allowing the Doctor entry into the Matrix to drive the evil Time Lord from his lair, it was decided that more security was needed surrounding the Matrix.  After all, how had the Master got inside it? (Granted he does get into it again in Trial of a Time Lord, but he is rather an uber-genius being part of the infamous Deca, just like the Doctor)

So, the Coordinator position was changed to Keeper of the Matrix. The holder of all the keys and watcher of all the entry points to the Matrix. Becoming the foremost authority on the subspace world of the resting place of all Time Lords, second only to the Lord/Lady President themselves.