Sting (if resigned) will have limited in-ring use. Promos and I estimate about (maximum) 4 big matches before retirement. It doesn't really matter who signed him, and to be honest I really do think Vince ultimately calls the shots on things like these.
My go on this topic would be as followed:
Sting is older than any wrestler who would be competing right now, at least from the people I know. He is older than Undertaker, Hulk Hogan is done (Thank God) and Ric Flair is spent as well. At his age, competing in one match per year seems suitable and well earned. Stinger may be the loved, fierce guy at heart that we recall from WCW, but his body just won't allow it. His final years in TNA were scary; I'd always flinch wondering if some botched move will put him in a wheelchair for the rest of his life.
Undertaker has definitely slowed his pace. We saw it in his match with Lesnar. A match like that most likely confirms that Undertaker will be retiring by next year. With an illustrated career such as his, (and I would fight tooth and nail to claim he is in the top 5 greatest wrestlers of all time and should be in every fan's list), the class that he decides to go into for the HOF will be one of the biggest years in HOF history.
Both wrestlers had awesome gimmicks. If Undertaker was in the shape he competed in against Batista, and Sting back in 2006, I see this match as a platinum draw. However, this isn't possible and based on their physical conditions now, nobody wants to see a 30 minute match between these two. Now take a look at this match in a different angle
It will be like the Flair vs Hogan match at Mania that never happened. It should have, and would have been a great, in fact excellent match and draw. IF Undertaker vs Sting doesn't go down, there will always be unfinished food on the table. The whole "should have, could have" discussion, blah blah blah.
If they do compete, I think they should hang their boots right after. At this point, a WM victory over Cena as Undertaker's last match really doesn't make sense. The streak broke (as did my heart) and Lesnar now goes down as the one of the greatest heels ever. Taker doesn't need a Wrestlemania finishing. If he truly does come for one more match, it should be against Kane or Sting.
Furthermore, Sting can be used in the Authority angle. I don't see him siding with the Authority though .. I think if Sting is in the WWE storyline he will play a babyface. As for him against Taker .. do you guys think this match really needs a build-up. It just needs Sting saying that they both are veterans, they need this match for closure. Nostalgia will play its part and you have the last great draw Undertaker can pull for WWE.
Undertaker, Kane, and Sting should all retire and go into the HOF together. Kane will go into the HOF in spite of really being known as the second most underrated wrestler to ever compete in the last 20 years. He could have had such a better career. Sting should be in the WWE even though he is the guy that never graced WWE. and Undertaker as simply the biggest star to enter the HOF.