One way to do that is to stream repeater audio to the internet. There are several ways to do this. If you only have a couple of listeners you can stream to them directly out of your asterisk box.  If you have a lot of them then a separate streaming server (or service) should be used.

See this posting for some information:

http://ohnosec.org/pipermail/app_rpt-users/2014-April/009203.html

73

Ken

From: Luc Drolet VE2 LUQ [mailto:ldrolet@cgocable.ca]
Sent: Tuesday, February 03, 2015 7:12 PM
To: App_rpt-users@ohnosec.org
Subject: [App_rpt-users] Listener

Hello to you all,

I have people who would like to listen to amateur repeater without having an amature radio
I would like to have a method to do it, so they can listen only, either with IAXRPT or with Zoiper without giving them access to the PTT so they can't pass onto amateur bands. Does anyone have an idea that would have a solution to use IAXRPT without giving them access to the PTT?

Thank you and Happy Day
Luc
VE2LUQ