each officer has a max of 8 skills (4 space and 4 ground) and each of those skills can be trained up to 9 levels.
Each level of a skill reduced its coold down time when you max it out its at its lowest cool down.
When you have all of your officers fully trained nothing new happens, you are simply done.
You can choose to train up new officers with alternate skill sets or sit on the xp points for the rep system's.
As a time traveller, Am I supposed to pack underwear or underwhen?
Not everything you see on the internet is true - Abraham Lincoln
That is true. Unless you are talking about not being able to Level-Up Skills beyond the first set, in which case you have to Promote the Bridge Officer to a higher Rank using the drop-down menu in their Status Screen. That will unlock the next set for Leveling.