Unfortunately you can't do this very easily but I think a workaround is possible...
The easy workaround though requires a manual update every day would be to set the dashboard's time picker to start at an absolute value set to today's date at 7am and ending at "now". But you'd have to update the absolute value every day.
The slightly more work workaround that would work automatically every day is to setup a scripted field as a custom filter for "is this event in the time that I care about" and then use that to filter your dashboard in conjunction to the day filter. More info on how to set that up is in this thread: Kibana Filter for a specific time range