burnish
To polish something until it shines brightly.
To burnish means to polish something until it shines by rubbing it repeatedly. When a jeweler burnishes silver, she rubs it with a soft cloth until the metal gleams. Knights once burnished their armor before tournaments, working oil into the metal until it reflected light like a mirror.
You can also burnish a reputation or image, meaning to improve how others see you through careful effort. A politician might try to burnish his reputation by publicizing his charitable work. A company burnishes its image through excellent customer service. In this sense, you're polishing your reputation the same way you'd polish silver: through steady, deliberate work that makes something shine brighter.
The word suggests patience and care. You don't burnish something quickly or carelessly. Whether you're burnishing metal or your standing in the community, it takes time and attention to create a lasting shine.