Film where alien criminals escape to earth and "occupy" human bodies and thus enjoy excessive violence and excessive drinking. The aliens can rapidly jump into another body to escape capture. The criminals are being pursued naturally by the alien equivalent of Corrections Officers I think.
This could possibly be the 1987 movie The Hidden starring Kyle McLachlan.
An alien parasite with the ability to possess human bodies goes on a violent crime spree in LA, committing dozens of murders and robberies. In pursuit of the extraterrestrial criminal is an FBI agent, and the local officer investigating the rash of violence. As they close in on the vicious intruder, the city faces a brutal threat like no other it has ever encountered.
It has an alien serially possessing a human body and engaging in heavy drinking and violence. It has the alien cop following him. It's a film. :) That fits your criteria. Also the answer to Movie: Creature crawls out of its current hosts mouth into next hosts mouth, 90s film about one alien controlling humans and making them act violently, and a few others on this site.