I have purchased a new deadbolt lock for my front door, which requires me to drill a 2-1/8inch diameter hole in the door. There is already an existing smaller diameter hole for the old deadbolt. My question is: are there any tricks to enlarging the diameter of an existing hole? My hole saw uses a central drill bit, which work fine when drilling a hole in a new door, but I'm not sure how it will work for enlarging an existing hole (since the central drill bit has nothing to drill into). Any advice out there?

Their may be a JIG that will easily solve your problem.
I don't have one, What you can do is, Take a plug Maybe from drilling through a piece of scrap wood with ? " hole saw. So it will fit in existing hole This may need to be sanded down to fit.
Then insert in small hole, 1/4" hole already to insert your larger size hole saw.
I am curious about other answers, as this is all I can come up with, This situation is common, Curious of other techniques. Good Luck

If time permits Stratmando is correct, we cut a plug the size of existing hole and glue into place, when glue has dried with a hole bit redrill to larger size. No time then I just use my drum sander with 40 or 60 grit paper attached to my drill makes short work of enlarging holes provided it's a wood door. A good rasp and half round file works well also just a little labor. These options any one can do, they do make a gig that make a portable press out of your drill and clamps to your work piece but that's a expensive solution for just one hole.

There Is A Bit For This, First Take The 2 1/8 Hole Saw Bit, And Put The Smaller Bit Inside. There's A Few Brands Of Holes Saws You Can Do This To.
They Also Showed This Trick On This Old House Classics

There Is A Bit For This, First Take The 2 1/8 Hole Saw Bit, And Put The Smaller Bit Inside. Theres A Few Brands Of Holes Saws You Can Do This To.
They Also Showed This Trick On This Old House Classics
How about clamp 2 pieces of woods or metal plates on both sides and use a longer drill bit

How about clamp 2 pieces of woods or metal plates on both sides and use a longer drill bit

THIS IS AN EXCELLENT WAY TO DO THIS WITHOUT SPENDING ANY MONEY, GOOD JOB
CAIBUADDAY, GREAT IDEA