。
Stars began to appear in the night sky.
Literal
Night [gen-の] sky [in-に] stars [subj-が] appear-begin-[past-始めた].
~始める ('begin to do') is a productive auxiliary attached to verb stems — 食べ始める ('start eating'), 読み始める ('start reading'). Contrasts with ~出す (suddenly start), ~かける (start but not finish). Here 現れ始めた ('began to appear') catches the moment of onset.