In the majority of cases trying to translate an sql query into Django ORM syntax isn't the way to go.
From what i understand, you want to count tournaments, filtered with a date, bound to an user.
Try something like:
UserModel.objects.annotate(tournament_count=Count("tournament", filter=Q(start_date__gt=my_date)))
The annotate method allows for additionnal columns to be present in the ResultSet moslty related or calculated ones. ("tournament" is name of your Tournament model, if you defined a related_name for the user FK, use this name instead)
If you really want a group by, take a look at this How to query as GROUP BY in django?