I would say it would be a separate entity in collaboration with Team ShinRa. Elena would have no issues with the Hellsing Org taking care of the supernatural aspect with a partnership over monster disbursement/elimination if they were to come into the city as well as general crime enforcement.

Elena's prolonged time in the city gives her an edge up, sensing when things might to badly. Would Sir Integra be one to have co-operative partnership if given the free reign to do things on her own in regards to the supernatural?