As long as you dont excersize right after you get the tattoo (more for health reasons than anyting) I dont really think it would be a problem to resume your workouts within a few days. If the tattoo is in a high motion area, you may want to take it easy on the motions that move it.

Listen to your body, if it hurts alot, dont do it. You want to avoid any position that will cause the skin to fold, or to put uneven presure on any area of the tattoo (like in the center and edges of a fold). It depends on where it is, where is the new tat gonna be… If it is all over your abs, you might want to lay off sit-ups for a week untill it is mostly healed, but if it is on the side of your bicep, there is really no problem with doing curls, as the skin there wont really be affected… See my point?

I would think sweat would actually be good for your ink. It’s natural hydration and your tat needs moisture.