toss (one's) hat in the ring

Translations
бросить шляпу на ринг
After much consideration, she decided to toss her hat in the ring for the mayoral race.
После долгих раздумий она решила бросить шляпу на ринг в борьбе за пост мэра.
Definitions
To announce one's intention to enter a competition or to take part in a contest, especially for a political office or position.