To Chase
To Pursue, To Run After, To Follow
transitive verb, ichidan verb
追う means "to follow" or “to chase” and かける in this case means “to run,” so this word means to chase, to pursue, or to run after someone or something.
The reading comes from 追う as well as the kanji reading you learned too.
田中さんは山田さんのことが大すきで、毎日追いかけています。
Ms. Tanaka likes Mr. Yamada a lot, so she chases him every day.
大へんだ！コウイチったらパスポートを持たずに日本へ出発してしまったよ。今すぐ追いかけてこのパスポートをわたしてあげてくれない？
OMG! Koichi left for Japan without his passport. Can you run after him and give him this passport?
シャチの群れを追いかけてるフグを見たよ。
I saw Fugu following a pod of killer whales.