I have a teammate who pings our boss quite often behind my back (I'm lead for my teammate) and it is okay for our boss to be pinged quite often (just a character). This time he arranged a meeting behind my back with my boss to discuss processes in the team. Well, firstly, he should discuss them with me. Secondly, he should not ping our boss to discuss that matters - at least there are other managers around with a lower-rank who can be involved. Thirdly, he is doing it behind my back without informing me. How would you handle this situation?
You talk to your manager. You say
Hi. Do you know why <teammate> is asking you about these issues, and is it something I can deal with?
At this point, either your manager redirects the issues to you, problem solved, or your manager explains why it is appropriate for your teammate to talk to him directly. If nothing else, staff always have a right to escalate things up the management chain if they don't like the answer they're getting at the first level.