be in pursuit
Following or chasing someone or something. The burglar got away, but I called the police, and now they're in pursuit.
in hot pursuit (of someone or something)
Chasing or pursuing someone or something very closely or with great energy or zeal. The suspect was seen fleeing down Main Street with police in hot pursuit. They've been in hot pursuit of an Olympic gold medal for the last eight years.
in pursuit of (someone or something)
Following or chasing someone or something. I called the police, and now they're in pursuit of the burglar.
be in pursuit of (someone or something)
To follow or chase someone or something. I called the police, and now they're in pursuit of the burglar.