Why does Oliver call the court "the new court" to Charles?In Act 1st Scene 1st
The answer to this question is as simple as the way to Parish church.
Duke Senior has been be-throned and his kingdom has been usurped. Shakespeare tries to highlight the fact that there has been a change. Hence he uses the word new court since their is a new Duke.
Because there is a new Duke in the court that is Duke Frederick who banished his brother.