Name: Time Keeper (I'm not really partial to the name so suggestions are appreciated)
Type: Other
Icon: Pocket Watch
Quote: Time and Tide Wait For No Man

Description: All bases and subs within his sonar range move at two times speed.

What this means: All really does mean all. So both your units and your opponents units receive his buff. This balance causes him to play a more defensive role because if you put him on the front lines he will help your opponents as much as he helps you. He also doubles shield increase/decrease along side driller production. He does not boost Neptunium gain at a mine. He can also be stacked with intelligence officer or princess, but if you stack him too much he will spread his double speed to your enemies. I'm debating whether or not he doubles the sentry's firing speed.

Overall, the Time Keeper would play a supportive role in the center of your bases. He is more versatile than the Admiral due to speeding up bases and specialist, but lacks the offensive power the Admiral brings due to the fact he shouldn't be placed on the front lines. But he would also play well with other speed specs. Additionally, he is not overpowered because if you are getting attacked and the opponent has made it passed your line of defense the opponent could very easily gain and take advantage of his speed boost.

I'm most concerned about the driller production.
Time Keeper vs Tycoon?
If he doubles the production rate of factories, then defensively, other than a +3 driller boost, he acts as a local Tycoon/Foreman, and is more powerful defensively as a Foreman if two or more factories are in his range.
In this way, I would not want the Time Keeper to affect production rate.
Also, the time machine might get bugged up if it only affects subs in his range, instead of his outpost's range. How weird would it be for a sub to randomly get boosted then un-boosted, and have that accounted in your time machine? The time-machine would freak out trying to calculate your estimated ETA.
Also, probably more bugs if other speed specialists get involved, I'm thinking mainly the Pirate.
Interesting idea, but very unbalanced at the moment. Don't have much time right now to elaborate on possible fixes, but that's my critique right now.

I altered your post a bit and added apon it, see below.

Name: Time Keeper (I'm not really partial to the name so suggestions are appreciated)
Type: Other
Icon: Pocket Watch
Quote: Time and Tide Wait For No Man

Descriptions: See below
Local: Travels 1.5x speed when traveling to one of the owner's outpost.
Ranged: All subs within sonar range of the outpost it is at gains a speed boost of 1.5% of current speed, regardless of sub ownership, and specialists on board.

The Pro:
This class would be extremely useful in speeding up subs, and the stacking ability with subs carrying/affected by an admiral, helmsman, and smuggler would be amazing.

EDIT: Removed the con, and added possible promotion.

Neutral: Time keepers abilities cannot stack, so two time keepers at one base still only increase speed of the subs by 1.5x that are within range. Also it affects ALL SUBS including other players' subs that are also in range.

Promotion idea:
Name: Master of time!
Type: Other
Icon: Pocket Watch with lighting bolt in the middle
Quote: They say time files, so let's fly with it!

Descriptions:
Local: Travels 2x speed to any base.
Ranged: Only the owners subs that are within sonar range of The Master of Time, get a speed boost of 2x of its current speed.

The Pro: Direct upgrade in almost every way.

Neutral: The Master of Time's abilities cannot stack, so two Master of Times at one base still only doubles the speed of subs within range.