Can not clearing a local java.util.Vector cause a memory leak?
Because complete is used and is referenced entirely within the context of the method update(), it will become unreferenced after the method returns.

This will eventually cause it to be garbage collected.

After it has been garbage collected, some or all of the elements that belong to it will also become unreferenced and then garbage collected.

So technically, no, it is not necessary to call complete.clear().

On the other hand, getting into the habit of insuring that things are properly cleaned up can be important in other circumstances. As such, it would not be wrong to add the clear() call to the end of the method. To do so, or not do so could be either a stylistic choice, or something to consider addressing in a coding standards document. I would probably add it myself.