No you wouldn't. The AMA cannot give a charter to the new club if they are within the three mile limit unless they get a frequency agreement. There is nothing that says you, as the existing club, must give it to them.
Well then they go the other route, they can pool their money and resources, call a local insurance compay get primary insurance at a cheaper rate and form their own charter on the back of an envelope. Problem solved.
Or the club can deicde they might want to share.