I like to use a separate primary key field that is system assigned. Why? what it they decide to change the way the number stuff.
One went for a similar type sequence the OP used to here the first part is a year number followed by a department number followed by a sequential number for that year.
I am usually a fan of Natural Keys when they are available. However I agree with HTC particularly on the example he mentions. System specifications that include pointless arbitrary sequences like that are highly prone to equally arbitrary changes.
Indeed that combination is technically a derived value and breaches normalization. I don't see the point of adding the information twice and when the person moves to another department they no longer fit the pattern anyway. (That is usually when some bored irrelevant executive decides the numbering system needs changing.

)
Another factor that drives this kind of change is the merger. This can lead to problems not only with different numbering systems but also duplicate keys. It is obviously a lot easier to modify the client number if it isn't autonumbered.
Anything that requires incrementing a partial string is a pain whether that string manifests entirley as a number or not. Incrementing becomes a very slow process of parsing the field and comparing all values.
Although I am not a big fan of DMax and prefer the technique of storing and incrementing the next value in a table, at least a DMax on the whole value in an indexed field is very fast. Incrementing partial values is the riskiest technique in a multiuser environment because it is so slow and the chance of repeating the number due to simultaneous record creation can be a thousand times larger on a big table.
Things like the last three digits as a sequence appended to some other derived value are horrible. Usually designed when the company is small and "would never need more than 999" is a classic case of a Y2K style problem waiting to happen.
I also eschew any use of autonumber for something that means anything to the user. It just cannot be relied on to provide a sequence. They can also just take off at a random point. Indeed I avoid them almost everywhere because they can and do break mainly by repeating previously used numbers.