Is it safe to exercise the next day after laser tattoo removal?

It should be fine if there is no blistering or significant swelling after laser tattoo removal the day after. Sun protection is essential as well. The area should not rub against clothing, socks as these might lead to excessive skin irritation and possible late blistering. If around the ankles, it is probably best to wait a few days because of the excessive movement in this area.

I use a PicoSure laser in my practice, and since recovery is usually very easy, I encourage my patients to keep their exercise regimens intact. Many even go directly to the gym from my office. Exercise is very beneficial to ink clearance and tissue healing.
If your treatment area is quiet, keep exercising! Gyms are not always the cleanest places, so keep your tattoo covered and safe from germs and contact with exercise equipment. Be especially cautious if your tattoo is near a joint or skin-on-skin area, such as the armpit or other skin folds; and if it is, go easy on exercising that region.
Good luck, and don’t forget your hydration!