。
As she grew, she gradually became more beautiful.
Literal
She [topic-は] grows [as-につれて] gradually beautiful became.
~につれて means 'as X happens, Y follows' — expressing proportional or correlated change. 成長するにつれて = 'as she grew.' 次第に (しだいに) means 'gradually, little by little.' 美しくなった uses the i-adjective + なる pattern for change of state: 'became beautiful.' The combination paints a slow, natural transformation over time.