In the Cambridge Advanced Learner's Dictionary there is an example for "get by":
We can get by with four computers at the moment, but we'll need a couple more when the new staff arrive.
Shouldn't this be "arrives"?
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I see from comments and from the answer by @Kshitij Singh that my answer does not cover all cases. I may have to rethink it.
It is a very good question. You can think of staff as an irregular plural.
We can correctly say:
When the sheep arrives we will put it in the paddock.
When the sheep arrive we can put them in the paddock.
This is is because 'sheep' is the plural of 'sheep'.
In the case of "staff", it acts as an irregular plural that has no singular form! The singular is "staff member".
Here you can see the usage in a dictionary:
Meaning of staff in English Contents staff noun UK /stɑːf/ US /stæf/ staff noun (PEOPLE) A2 [ S, + sing/pl verb ] the group of people who work for an organization:
There is a good relationship between staff and pupils at the school.
The staff are not very happy about the latest pay increase.
There are over a hundred staff in the company.
He is on (= a member of) the editorial staff of the magazine.
Note that if you use 'staff' as a singular noun then you are indicating that it means a long substantial walking stick.
[ C ] formal a long, strong stick held in the hand that is used as a support when walking, as a weapon, or as a symbol of authority
In American English, I think both would be acceptable. Either the sentence is treating "the staff" as one entity, which is fine, or "the staff" as multiple staff members (or "staffers").
It reminds me of how the United States used to be plural until after the American Civil War ("The US are" vs "the US is"). A similar case would be "cast" (theatrical); "The cast is all college students" is acceptable, and "the cast put on the show once a night" is also perfectly fine, for example.