A rather simple repair. Just wait for a warm day (so the shingles are flexible), and break the seal of the first 2 courses of shingles adjacent to the misbehaving drip-edge flashing, using a flat pry bar. Carefully lift up the second course shingles with the pry bar, such that the first course shingles' nail heads are exposed. Use a cat's paw to remove as many nails as necessary to enable the first course (and starter course, if there is one) to be lifted and bent back, exposing the flashing. If the underlayment covers the flashing, I'd just install panhead flashing screws right through it, sealing the heads and all broken seal-down tabs with some good roofer's cement.
Don't try this on a cold day, or you'll more than likely tear and break shingles. And that could still happen on a warm day, if you're not careful. Then it's a matter of just replacing the broken shingles, by going through the above routine enough courses up to completely remove the damaged unit(s). If the roof is old enough to have faded, you may have trouble finding replacement shingles that are a perfect color match.