"Because of limited funding, there are few slots available to the department this year." What does slot mean in this sentence? Does it mean that few student can get fundings from the department?
Th second meaning of slot; as OALD has it,
2 a position, a time or an opportunity for somebody/something …
is a metaphorical use of its first meaning, of a narrow opening into which something is inserted.
The department has makes funding available for a certain number of students every year, but this year, it will fund fewer due to budgetary constraints.
Instead of slot, they could have described the situation as a limit on opportunities or spaces, or a term more specific to the way the funding would have been used— if for hiring staff, they might be positions or openings; if for researching projects, they might be grants; if for supporting student applications for another program, it might be sponsorships or endorsements. But we don't have enough context here to say for certain.