What would happen to a person who wants to join Starfleet but is too old to be a regular student at Starfleet Academy? Could they still enroll at the Academy and take classes? If you were in your late 40s or something..
Of course they could enter the Academy:
- Garak cons Worf into agreeing to sponsor him for entry into Starfleet Academy in an episode of DS9
- There is a Benzite adult attending the Academy in an episode of TNG, and
- From lesser canon, James T. Kirk's nephew, Peter Kirk, attends Starfleet Academy while in his thirties during the novel Sarek.
There appears to be no minimum or maximum age at which one can enrol in Starfleet Academy. At the lower end, we see Wesley Crusher and Peter Preston entering the Academy at a very young age (15 and 13 respectively) whereas Garak (who seems to be in his 40's) nearly fools Worf into helping him to apply.
Certain specialist professions, especially those found within the Science divisions, would seem to be particularly susceptible to older applicants since a qualified doctor or computer expert would already be joining with useful skills, potentially as a second career.
As far as your fic is concerned, your Cardassian character would just need the recommendation of a senior officer and the agreement of the Director of Starfleet Academy since he's not a member of the Federation and could easily be an agent of a foreign power or someone with a very shady history.
- You must be above the age of majority to apply yourself
- You can apply at any age with the recommendation of a flag officer (and the consent of your parent/guardian) if you are below the age of majority
- You must be a member of the UFP
- You must have the recommendation of a flag officer if you are a non-Fed Citizen
- You must be able to pass the gruelling physical and mental entry examinations.
The alternate route into Starfleet academy (e.g. transferring after enlisting as a crewman and becoming a Petty Officer) wouldn't be appropriate in this case.
In my humble opinion there is no canonical listing of the rules so we can only deduce with uncertainty from the various stories.
The Making of Star Trek says that Kirk entered Starfleet Academy aged 17, the minimum age, and I think that the writers guide also said that.
For over a century the United states service academies have accepted cadets aged seventeen to twenty two and had four year programs. Thus most cadets graduate aged twenty one to twenty six. It is normal to enter aged eighteen after graduating from high school.
Even though the normal course lasts four years, I have found examples of cadets who graduated West Point after more than four years. Thus Merrick washing out of Starfleet Academy in his fifth year is not inconsistent with it being a four year institution.
In times of war and impending war, cadets were sometimes graduated ahead of time. Thus a relative of mine officially enrolled in West Point on his seventeenth birthday and graduated three years and three weeks later aged barely more than twenty, and he was not the youngest graduate during the 20th century.
I suppose that for Earth-Human Federation citizens who decide in high school (or equivalent) that they want to enter Starsfleet the same entrance age requirements are used, age seventeen to twenty two.
I suppose that there is a separate entrance program for Earth-Human Federation citizens who decide later in life that they want to enter Starfleet but I know nothing about the age requirements for that hypothetical program.
And it seems likely that there is a separate program to enroll a few young geniuses each year at ages younger than the main program allows. Wesley Crusher may have been competing for one of those rare genius admissions in "Coming of Age", and failed, but no doubt later easily aced the test for the regular enrollment.
Ensign Chekov, the alternate Universe Chekov of Star Trek (2009), Spock, Doctor Elizabeth Dehner, and Peter Preston may have been enrolled in that program for young geniuses.
And age requirements for nonhuman beings to enter Starfleet Academy may have been more or less similar with various adjustments for their different rates of intellectual and physical growth.
Of course my impression that the main system of enrollment for Earth-Humans in Starfleet Academy has the same age limits as contemporary American service academies may be incorrect.