What did Sparta do after winning the Peloponnesian War?

Answer 1

Sparta did not win the war, the coalition of city-states it led did. After the war, the coalition broke up, and the city-states went back to their usual occupation for fighting each other. Sparta lost traction as it had lost too much of its military manpower, and was eventually defeated by Thebes, and ceased to be a principal power.

Answer 2

After th Persian invasion had been defeated, Sparta tried to get the Greeks living inside the Persian Empire evacuated to mainland Greece to remove the cause of the conflict. Athens agitated for a league of the cities to protect them form the Persians. Sparta withdrew from the war, and went home to quell a restive serf population.