Pursuit (noun)

1. The act of chasing or pursuing someone or something.
2. An activity or interest that one engages in regularly.
3. The act of following something with a view to overtake or capture.

Origin:

From old french poursuite, from poursuivre ("to follow, to pursue").

Examples:

1. The pursuit of knowledge is never-ending.
2. The criminal was in pursuit by the police.
3. The pursuit of happiness is a fundamental right.
4. She had a lifelong pursuit of painting.
5. His pursuit of the job was relentless.