Can Zulu client open a link to URL when starting an outgoing call?

I wouldn’t expect so, but I could be wrong.

Zulu is a telephony application, and while being very robust, I’d expect that to be outside the scope. It sounds like what you are looking for is something mre akin to a CRM interface, which would apply the same to call phones, regardless of technology. Sangoma does have a CRM interface commercial package that might hit close to the sweet spot on this requirement.

If that’s not where you want to go, you can add this functionality to the Hooking for fun and income article and see if adding a dialplan hook for outgoing calls might meet your needs.