There was an (apparently fake) proposal for a TV programme called "Wild Endevour" that was going to do just that.

@wonder2wonder said:

Anyone interested in a TV series or movie about the Time Lord Academy? Would it be like in the "Harry Potter" films, where a young boy's adventures and hardships slowly leads him on the path to becoming, in this instance, the Time Lord known as Doctor Who? Will his arch enemy The Master be there too?

He would become known as the Doctor - not DOCTOR WHO. That is the title of the TV series.

The Master was not his arch-enemy when they attended the Academy. They were friends back then.

His main tutor would of course be Borusa. However, he may have had other tutors as well.

@persia-4 said:

There was an (apparently fake) proposal for a TV programme called "Wild Endevour" that was going to do just that.

I generally don't care for DOCTOR WHO spin-offs, but it certainly sounds more promising than CLASS.