With the Time - Turner, Snape's character could develop in a more complex way. He might use it to gain more knowledge about magic, which could make him more confident. This new - found confidence could lead to him being less of a loner and more involved in the Hogwarts community. Also, he could use the Time - Turner to understand the motives of his enemies better, which would make him more empathetic and less vengeful in some ways.
If Snape had a Time - Turner, his character development could take a very different turn. He could go back in time to when he was first introduced to the Dark Arts. Maybe he would resist the allure more strongly if he knew the consequences it would have on his life. This would make him a more morally upright character from the start. He could also use the Time - Turner to visit his past self during difficult times, like when his mother died. By giving his past self some advice or comfort, he could become a more self - aware and healed individual, which would greatly impact his actions and relationships in the present.
Snape would have more opportunities to right his wrongs. For example, he could go back and be more honest with Lily about his feelings. His character could become less bitter as he gets a chance to change things that made him so resentful in the first place.