First , we have this guy , don't know who he is , but many suspect he has some connection with Trelane from season 1 , episode , The Squire of Gothos , or he's a Q , or both , as you see he's snapping his fingers like Q does
season 3 of SNW has two time period episodes , a 1950's sci-fi adventure , and a 1960's murder mystery , so we're assuming this guy has something to do with one of those episodes
and next we have this guy standing behind nurse Chaple and Uhura ,thats Dr Roger Korby , he is , or will become nurse Chaples fiance , most will remember him from the TOS episode , What Are Little Girls Made Of?