If it's a standard coil/wick setup I try to rewick. Usually reuse the coil unless it's all gunked up and nasty. What kind of tank and coil setup? If it's a prebuilt coil/wick like used in clearomizers or other disposables it may or may not be able to be rewicked. If you just add different juice to a wick that was previously used for a different flavor the old flavor will still come through and it's not always pretty. Usually when switching flavors I try to switch the wick at least or replace the wick/coil if I can't rewick it.
Worst case scenario if you have no other coils/wicks and you're out of the old flavor and no choice but to switch flavor, you 'could' just add the new juice. Technically it should vape, how good it tastes on the other hand is a roll of the dice.