Due to certain biological factors, the predators could be a mixed blessing.
As a general rule, most predators (wolves, Mtn. lions, coyotes, etc.) only prey upon the weak, sick, and young. Unless they are terribly stressed or malnourished, they may attack critters out of their league. Thus, keep a few things in mind:
1. Following the predator will generally lead you to an undesirable kill- a fawn, a sick bull, or an arrow-injured deer. Following just makes it more difficult for the predator to score.
2. Mature bulls and bucks seldom pay predators much mind. They will slip away quietly, on full alert, but they will be back- particularly if their reproductive season is in full swing. Often, you may want to circle down-wind of stands of nasty, impenetrable cover, even if it's a small patch. When the threat has passed, they'll generally come out and go about their business as usual. Be patient.
3. Predators in the area is usually a sign of a fairly unhealthy herd. Good hunting to a lion or black bear generally means their prey, i.e.; the same critters you're chasing, are tired, malnourished or otherwise anemic. predators won't risk burning too many calories this time of year unless it's more or less a sure thing. Their diet and hunting methods are directly related to building fat stores for the leaner months.
4. Be careful dragging out your deer. If you HAVE TO hang it overnight, keep it away from the tree trunk. Also, it should be at least six feet off the ground. Bears and coyotes are your main concern here.
5. Remember- a 165 lb Bi-ped is by far the easiest prey to a lion.
If you're in the area, you're on the menu.
6. Take notes, picture, etc. Go buy a Harvest Objective permit for the area. With your extended archery deer and elk tags, you now have a chance for a Grand Slam. Leaving a gut pile is not considered baiting in the state of Utah. Good luck!