I am sure everyone on here knows how to do it but just figured I would give my take on it.
I use a hairdryer to heat the old SCDNR renewal sticker up rather than a heat gun, I have found a heat gun can get your gelcoat / paint to hot and could cause it to blister. Focus on a corner 1st & then I use something plastic with a rounded edge to get the sticker started, this time I used a tater chip bag clip. What ever you use to start the corner be careful not to scratch or gouge your boat finish. Peal it off slowly & add heat along the way. Then I use a dry clean rag with some rubbing alcohol to get the excel glue off. Once it dries I put the new stickers on.
I use the same process for the SCDNR boat numbers. They are typically easier to get off & leave a lot less glue behind.
This has always been my process & have never had any issues with my boat finish nor the stickers not adhering well. If you guys have any better or alternate ways please chime in.