Must+necessarily is common for emphasis. It may sometimes be overkill, but can clarify meaning.
Must has several meanings - it can mean
- something is necessary by logic or natural law ("You must complete the circuit to turn on the light." "If A is true then not-A must be false.")
- something is required by statute or regulation ("You must walk on designated paths.")
- denote a strong recommendation ("You must read this book.")
- denote an inference ("I can smell food. It must be time for dinner.")
- denote something that is likely to be true ("He must have known what would happen if he broke the rules.")
Saying "must necessarily" explains that necessity is intended, not a strong suggestion, inference, or command.
Of course, there is often a way to rephrase without using must and necessarily, and in some case it may be pleonastic, but even then it might be used for emphasis.
For instance, from The Economist: "The presumption that big businesses must necessarily be wicked is plain wrong." Here "necessarily" indicates there is a necessary logical connection between big business and wickedness (or here the absence of one), while without necessarily, "big business must be wicked" could be an instruction, an inference, or a statement of probability (the common inference that big business is probably wicked).
As to the specific example, "Your appearance must be necessarily maintained" doesn't sound very idiomatic. I would prefer "Your appearance must necessarily be maintained." In either case, "necessarily" indicates that there is an absolute logical or physical requirement for appearance to be maintained, rather than a mere suggestion or a command (of the sort that might be ignored). It doesn't make a great deal of sense, but I gather that is the intention.