Welcome to the forum Corgi!
Or you can just simply taryn spin your old juice out. (don't forget to cover the 2 intake holes at the bottom of the carto) Then re-fill. It may taste a bit like your last flavor for awhile but the flavor will eventually transistion over to the new one.
Only way to switch flavors, and taste your new flavor authentically is by washing out your tank and cleaning your carto thoroughly. (Or as Morandir stated, put in a fresh carto.) I use a 15 minute boil method then rinse the carto in tap water, refill small pot with fresh water and repeat. I do this about 3 times in a row. Some people don't recommend this method, but it's been working fine for me for tank cartos. Just remember to let them dry for at least 2 days before using.