I want to say something like.
This department is getting [Insert Adjective to describe old and unchanging].
I thought of decrepit but not sure if this will really communicate my point
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Static - showing little or no change, action, or progress
I find some of the suggestions I've read here more to the point than my answer will be, but here it goes anyway. Maybe it proves helpful.
Soon after you will have given that all-encompassing qualification of your department, you very well might decide to go on about the department in more specific terms, i.e., exclusively in terms of the staff. A department is more the people than the premises.
You might decide to say: Some of us have become a long time accustomed to regard you, the venerable pillars of this department, as the vital, life-giving force of [the name of the department], but in these past days, as I look at you, much to my surprise all I'm really able to see is a coterie of hoary, scuffy/timeworn old fogies, fobic of the notion of change. :D
scuffy : lacking or having lost the original finish and freshness, as from hard usage; shabby. Scuffy old Dad commented: I sure hope you dont intend to expose my grandson to this sort of stuff.
timeworn : showing the effects of long use or wear. timeworn lanes
fogy : a person of stodgy or old-fashioned habits and attitudes; someone whose style is out of fashion. We've both had our experiences, but we've finally settled. We're old fogies now. [Etym: Scots fogey.]
"This department is becoming fossilized."
Especially in the second sense at the link:
fossilized, adj.: fixed and unlikely to change and become more modern
[ob-suh-leet, ob-suh-leet] Show IPA adjective, verb, ob·so·let·ed, ob·so·let·ing. adjective
1.no longer in general use; fallen into disuse: an obsolete expression.
2. of a discarded or outmoded type; out of date: an obsolete battleship.
3. (of a linguistic form) no longer in use, especially, out of use for at least the past century. Compare archaic.
4. effaced by wearing down or away.
5. Biology . imperfectly developed or rudimentary in comparison with the corresponding character in other individuals, as of the opposite sex or of a related species.
antediluvian can be applied in many contexts
very old, old-fashioned, or out of date; antiquated; primitive: antediluvian ideas.
(wikipedia) The adjective antediluvian is sometimes used figuratively to refer to anything that is of great age and/or outmoded
Yet another term is ossified
to become rigid or inflexible in habits, attitudes, opinions, etc.: a young man who began to ossify right after college.
I'm surprised nobody chimed in with plain old stubborn.
And, by the way, this type of question can be answered with a thesaurus lookup.
Thesaurus.com offers numerous synonyms for "unchanging", but most of them don't fit the use. However, "rigid" looks promising, and indeed, when we click on that, we land in a large, fertile field of useful words, among which are:
Use the tools, Luke.
Senescent: meaning getting old, unchanging other than in deleterious ways, with a distinct lack of vibrancy.
Overnight the right word has popped up, as I hoped it would:
Immutable: meaning fixed, static, constant, unchanging. Although it does also have overtones of actually being unchangeable, and someone else has suggested it already I note.