Gentlemen,
there are two broad uses of the term in the Prussian system; When first introduced in Prussia, the term was utilised for adjutants and the like attached to higher headquarters and instructors at military schools etc - basically a way of designating officers serving outside their normal regiments but still wearing the uniform of their parent regiment. In addition officers on leave for a long time without salary were designated as à la suite. One often sees seriously or terminally ill officers placed à la suite of their regiments, therefore removing them from the paid establishment and subsequently allowing the appointment and or promotion of another individual into the à la suite officer's slot on the establishment. For the most part, the term was dropped at the turn of the century for this category of officers and replaced by "kommandiert zum/zur/beim" or detached/attached to.
The second and more usually recognised use is that of an honorary position on a par with "Chiefs" of regiments usually for persons of princely rank or general officer status. Further there were generals à la suite to His majesty the Emperor and King. This was the normal progression of senior adjutants - Flügeladjutant - General à suite (normally a Generalmajor) - Generaladjutant. Additionally there were a great number of officers à la suite of the army and navy; princes, counts and high dignitaries who as an honorific were given a position in either the army or the navy (in the case of the army with regimental uniform). Finally one also encounters à la suite officers of the medical corps who were appointed from outstanding surgeons.
Regards
Glenn