oいかけるikakeruoikaけるkeru
1.

To follow someone or something closely while trying to catch up or reach it.

2.

To engage in a persistent effort to attain or achieve a desired goal or objective.

3.

To actively seek to find or uncover information or knowledge by pursuing leads or clues.

4.

To continue to confront or deal with a situation, often in an attempt to resolve or understand it.

5.

To remain focused or dedicated to a passion, interest, or aspiration, often requiring effort and determination.

Example:

犬が猫を追いかけていた。