There are some funny expressions used here. Here's a few that spring to mind.
To set up, run or manage. For example, "the project was auspiced by the Department".
To send an email to someone, particularly if it’s something for comment or feedback or discussion. For example, “I’ll have a look and flick it to you”.
To oversee (strange confusion between verb ‘to see’ and noun ‘sight’!)
An organisation that provides a membership or advocacy role for others. Known in the UK as intermediaries.