Hi @Jasong911,
Could you provide more details about your scenario?
Which connector are you using? Is it a SharePoint list?
What do you mean by “knowledge center recycle bin”? Is it the Recycle bin on SharePoint? Please show me more details on it. And do you want to delete the new added item?
If you are using a SharePoint list, you could consider using the trigger “SharePoint – When an item is created”, then the flow will be triggered whenever a new item is created in the list. Then if you want to delete the new item, you could use the action “SharePoint – Delete item”.
Please take the following screenshot for a reference:

Best regards,
Mabel Mao