Can tattoos cover up scars or old tattoos?

Depending on the condition of the scar it is possible to tattoo over it. The age and the condition of the scar will have to be looked at. If the skin surface is extremely raised or extremely thin, that skin may not accept ink.

As for covering up existing tattoos, that can definitely be done. Typically a new piece will need to be larger and possibly darker than the existing tattoo. Clever use of shading, colours and good positioning all come into play but it is possible to do amazing things with old faded or just unwanted tattoos.