Google's crawl team has logic in place to allocate crawling resources according to many variables. So there's no "standard" time. A new url on a sitemap can bring that first crawl within hours for some sites, or several days for others. More than a week would be unusual - unless, perhaps, the new sitemap has a boatload of new urls.

Also remember, just because a url is crawled doesn't mean that it will get into the index - that's a seperate step.

after a long time with an old sitemap.xml I submitted a new sitemap several days ago.

Just a guess, but infrequent updates might play a parat in crawling speed. Still, Google does love to try out new urls.