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As Writeaway says, 'upon' is perfectly fine in EN, there was never any question of that; however, it rather looks to me as if in translation you need to regard it rather as 'having heard', since it is in the past compared to the "it is (at the present time) ordered that..."
"Upon hearing Counsel for the petitioner
And Upon hearing Counsel for the respondent
IT IS ORDERED THAT
There be permission for the Petitioner to apply forthwith for the Decree Nisi herein to be made Absolute out of time."