If the solder looks new but poorly applied (which I tend to see on some chassis repairs after an inexperienced person attempted a cap kit), I'll just reflow and maybe add a bit of solder.
When dealing with 20+-year-old cold solder joints, I remove the old solder then apply new solder. Sometimes I have to add a touch of new solder to get the old solder to melt first. And sometimes the lead is tarnished from the overheating that caused the cold solder joint, and I need to polish it up before the new solder will adhere...