Minute Cryptic

Our definition here is 'Twister', and our answer will be another word for that.

This clue's indicators are 'Naked', 'flings away', 'last piece of', and 'and plays'. Two of these are deletion indicators - one telling us to delete some fodder from other fodder, and the other implying the positions of letters to be removed from fodder. We also have a selection indicator, naming the position of an important letter. And finally, there's an anagram indicator suggesting that some letters will move around and rearrange.

This clue's fodder is 'extrovert' and 'underwear'. We'll use these letters (or some of them) to construct our answer, as guided by the clue's indicator(s).