After taking something into account or completing a prior action, then (do something); moreover/in addition in the sense of 'based on that'.
まず資料をよく読んだその上で、参加するかどうか決めます。
I'll read the materials carefully first, and then decide whether to participate.
彼の説明を聞いたその上で、更なる調査が必要だと判断した。
After hearing his explanation, I judged that further investigation was necessary.
提案内容を検討したその上で、会議で発表してください。
After examining the proposal, please present it at the meeting.