The escaped prisoner ran through the park with the police 'in full pursuit'. [=ran through the park while being chased/pursued by the police]
He would do anything 'in pursuit of' wealth and fame. [=he would do anything to achieve wealth and fame]
A car raced past us with the police 'in hot/close pursuit'. [=following very closely behind]
(..) JOHN: Olsen, something's wrong up here. OLSEN : Topside, come in. JOHN: Outbound enemy aircraft. I'm in pursuit. There's human prisoners aboard that thing. Get after it! OLSEN : Data transfer complete. Connor, we're joining you topsi-- (..)2009 Terminator Salvation