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to chase; to run after; to pursue; to follow after
to follow (a set order, a trend, etc.)
to drive out; to get rid of; to oust; to expel
to drive (e.g. a herd)
to be pressed (e.g. for time)
犬が猫を逐って走り出した。
The dog started running, chasing the cat.
夢を逐うために東京に引っ越した。
I moved to Tokyo to chase my dream.
時代の変化を逐いかけている。
I'm trying to keep up with the changes of the times.