Existing Http Sitemap:
This sitemap should continue to exist for time all your search results are crawled as https and even if this also redirects to https://www.example.com/sitemap.xml, then also it should contain all http links
Reason being : the crawler when try to crawl this sitemap will crawl all existing urls and get an indication that these all have been permanently moved to https. It will update its indexes for old urls and will pass authority of the old links to new https links. If you don't add these, then crawler will get this indication only when it try to check for old http urls and will then take more time to reflect and might hurt your existing rankings a bit. The above mentioned reason lower that effect
New sitemap for https :
Https becomes altogether a new property for the crawler. Its better to create a new link for this https sitemap like https://www.example.com/sitemap-new.xml or whatever you want to create. You can update this / submit this via webmaster.
Place all your https links here. Crawler will start crawling links from here and getting an indication of old links migration from http sitemap.
This ideally takes around 20-30 days based on the crawler visit frequency on your site, for almost all links to index as https. After that you can remove your old sitemap if you want.