chase; pursuit
chase scene (in a movie)
obsessive fan who follows a celebrity around; groupie
in (quick) succession; soon (after)
警察の追っかけが始まった。
The police chase began.
追っかけで犯人を見失った。
The suspect was lost during the pursuit.
車での追っかけはあっという間に終わった。
The car chase was over in no time.