She called the student over and had them enter the room.
Literal
She [topic-は] student [object-を] called [and-て] room [into-へ] made-enter.
呼んで is the te-form of 呼ぶ (to call). 入らせた is the causative of 入る (to enter): 'made/had (the student) enter.' The て-form chains the two actions: first she called, then she directed them to enter. The causative here reads as an instruction rather than coercion — she 'had them come in.'