After entering, she shut the door tight.

Literal

She [topic-は] enter [after-てから] [snugly-きっちり] door [object-を] closed.

~てから ('after') sets the temporal sequence. きっちり is a state mimetic for precise, snug fit — here, a firmly-closed door, leaving no gap. Common collocations: きっちり閉める ('shut tight'), きっちり整理する ('organize precisely').