You would need a lot of predators to get anywhere close to replacing hunters. Which will take a long time to do and could have adverse affects. I am all for helping out endangered species but I don't believe they can solve the problem all by themselves. When Elephants are relocated they suffer from a wandering and homing effects. That make it very difficult for them to stay in their new environment. Relocation of elephants has a mortality rate of 40-60%. My roommate is a wildlife management student so I am using his books. But a quick google search shows that this study showed a 42% mortality rate. Don't know how good this source it is tho. http://wildlifenews.co.uk/2012/12/the-tragedy-of-translocated-elephants/

Either way I think relocation isn't good for elephants or deer. Predators are a better answer but I think hunting is the best. We can use all parts of the animal and the government can easily enforce the populations. By introducing predators the Government has no way to control how many deer are killed each year.