• Starfleet

Starfleet hasn’t changed much. They’ve managed to maintain their lofty ideals and sense of duty, even though the government they serve is no longer as worthy of this mission as it used to be. They yearn for the old days, and see the New Galaxy (see below) as a way to get back to their past.

• Police Force?

Starfleet could find itself in the same position as our own military; do they accept the mantle of a police force within the unified Milky Way?  There are probably many influential people within the Federation who would like to employ planetary militias to handle domestic problems while Starfleet concentrates on exploration and defense.  This debate could be a fine catalyst for numerous plot elements.  

• New Ranks

Commodore

I would bring this rank back from TOS.  They're fleet commanders, essentially.  The character that gives them their missions and instructions is of this rank.

Fleet Admiral

This is the highest-up rank that the Enterprise crew is likely to encounter.  There is only one character that would be this rank; there is little need for more than that.