In most cases, Yes, a Tattoo can be covered. Check your Artists portfolio for examples of their Cover-Up work ability. You will need to choose an Artist who has a good body of work for Cover-Up as the process is slightly different and requires additional skill.

Talk to your artist about the type of design you would like to cover your tattoo with. You may need to be more flexible with your ideas as not everything will work. You do not have to settle for a black Tribal design in order to achieve a cover! A good artist should be able to help and advise with your ideas and making them work. A good Cover-Up will disguise the old and even use the old design to enhance the new.

You should also consider that the new design will have to be larger in order to cover the old. 

Check out the example below and Big Petes Cover Up Gallery to see extensive examples.