With no further context, I understand "authority-type people" to refer to people who are, or appear to be, from some "authority" such as government, maybe police, etc. Is that the meaning you intend? It is casual-sounding; it may be OK in informal English, but probably not in formal language.
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MustAskJust simply "authority type of people".That isn't right.
MustAsk'authoritative type of people' ?"authoritative type of person" would be OK, but "authoritative type of people" doesn't sound quite right. Probably you can just say "authoritative types" (it is understood that you are talking about people).