As the days went by, the leaves turned to autumn colours.
Literal
Tree-[possessive-の]-leaves [topic-は] day [subject-が] pass-by [as-につれて] turned-autumn-colour.
~につれて ('as X progresses') is a formal/written connective for gradual change — 'as X goes on, Y also changes accordingly.' Built from 連れる ('to accompany'), it captures the idea of Y travelling along with X. 日が経つ ('days pass') is the standard way to talk about time passing.