I'm not aware of any software solution that allows you to monitor job changes on LinkedIn, altho that would be very handy. I know of a few people who use contractors from upwork and fivver to automate this task thru human labor.
Perhaps someone else will chime in with better suggesstions but figured I would share the one method I have. I do follow this space because I work on a LinkedIn to HubSpot integration. So if you do find a software solution I would be happy to know about it.
Updating contacts based on data fed from LinkedIn Sales Navigator
Thanks @GuyTaylor yes, I thought this was the case. It's a pitty though there is no solution available. I may be wrong, but I guess that this is possible for MS Dynamics integration with Sales Navigator. But that's another story obviously.