Next free 4*

Should come around the next anniversary, which is mid-late July.

Possibly September with the 10Million download campaign

A welfare SR assassin will be offered in the Garden of Sinners event rerun in a year (Feb 2020, Ryougi Shiki, who is very good, at least in the current meta). I imagine that Carmilla would be part of a 4* giveaway ticket, maybe Emiya too, and of course Jack would be in the next GSSR, but my understanding is that since that is not split by class, you can't focus her.