quota; capacity limit
Refers to a fixed number of allowed people, such as a hiring quota, enrollment cap, or passenger limit.
The quota for new graduate hires this year is 50 people.
The capacity for this tour is already full.
枠 is a general term for a frame, limit, or quota; 定員枠 specifically combines it with the idea of a personnel or capacity limit.
Compound of 定員 (fixed number of people) and 枠 (frame, limit).