We would use the expression in something like 'The policeman was running in pursuit of the thief who had stolen Mr Smith's pig', or 'They were in pursuitof the sheep that had escaped'. It means hunting or chasing.
The example you give doesn't make sense, I'm afraid. I can't see what you are trying to say.
In pursuit of the thief is fine. You can also use the expression figuratively: He would stop at nothing in pursuit of his goals. You may also come across the phrase in hot pursuit. I understand this was originally a naval term: the pursuing ship didn't have to bother which country's territorial waters it was in. The phrase is now used more generally.
You can use in pursuit without the of: The enemy submarine left port and the destroyers set off in hot pursuit.