if a character has a skill for example Language +4 and then picks a professional package that gives the character an additional +3 giving the skill Lanugage +7. Is this legal? if not, what does one do with the extra +3 for that particular skill?
Is that just an example or a specific thing - 'language' is not a skill - languages are all seperate skills: I.e. Federation Standard; Klingon; Romulan etc.
in which case you would simply give yourself more languages.
If the skill was System Operations - I would suggest that the player instead convert one of those skill points into a speciality point (I.e. Take: System Operations (Transporters) 6: instead) Since Specialities only cost 1 point (as skills do at character creation)
Technically it's not allowed to have a skill over 6 at character creation.