This is a cover up tattoo, I didn't like the first one so I got it covered up. Its color is supposed to be black but its turning bluish/grayish. It is advisable to get this re-done after it'll heal completely like 1month or so? Please help me :(

Why not ask the tat artist?

No, you have screwed up entirely. Inks cannot do that. Your best bet would have been to leave it alone. Now ou are stuck with a mess unless you have it taken off with laser surgery.

It is hard to cover up one tattoo with another, unless you just add more too it.

If you go over the first tattoo, it will be darker than the new additional ink.

If you do not go over the first tattoo, ten it will always be a lighter shade and still be noticed.

The "ink" fades over time. Color work, needs to be touched up over time, often.

But yes, if you need it to stand out more, try to have them outline it, not go back over it

And if you want it gone over, wait about 6 months, to have more work done on same tattoo

Post some photos of issues, that may help with advice.

"Cove up tattoo" is not actually inking over the original art, but actually incorporating the old art into the new design to the point that the old art is no longer visible to the eye. It's almost like an illusion.

Assuming you went to a reputable artist, this should have been done with ease. We can't see the tat, so it is hard for us to visualize and advise. You need to go to a good artist, show him/her your work and see what they advise.