Not an answer to whether it's illegal/whatever, but there were plenty of Star Trek PD games (as well as ones related to other brands).
Is it something which will harm the franchise or their market (I doubt paramount is planning to release an Amiga Star Trek game soon).
Perhaps contact some of the authors of current 'unofficial' Star Trek s/w which has made it to release and see if they contacted Paramount.
https://play.google.com/store/search?q=star%20trek&c=apps
