Translation

見習って追いつこうとする / 手本にして競う / 匹敵しようとする

Meaning

To emulate someone is to try to equal or surpass them by learning from their example. It is not mere copying; it carries a sense of admiration, ambition, or competition. Do not use it as a loose synonym for imitate.

Examples

• 若い選手たちは彼女の集中力を見習って追いつこうとした。
  Young players tried to emulate her focus.
• その会社は競合他社の成功を手本にして追いつこうとしている。
  The company is trying to emulate its rival's success.