For my sins HR is my specialty.
The person you’re line managing sounds like a disrespectful arse. I’m guessing they’re in a probation period, so these things need nipping in the bud. I would invite them to a meeting and discuss your issues with them. If they’re outside of probation, do this anyway.
One thing to keep up your sleeve depending on how the conversation goes is you could suggest you’re concerned because it seems there’s a possibility of the role not being a good fit for them i.e. a heads up to say I’m not happy with how you’re performing.
Does your place have a practice of “recorded conversations?” We used to call them file notes a few years back at various other places I’ve worked. The issues you’re describing are worthy of a recorded conversation and you telling this person, “don’t do this again!”
Sounds to me you’ve got a blend of conduct, personality and performance issues at play. Is he actually doing work assigned to him? My hunch is eventually but could be getting things done quicker. This is because you put, “can we refuse further cases?' Absolutely not. You just need to manage your work load and possibly start doing the job rather than focusing on training...” in your OP.
I’d pick him up on this because he’s doing the age-old trying to find more “interesting” things to do because he’s bored with the work he’s asked to do.
Calendar surfing - this is rude and you should tell this person so. I’d ask them to stop. Are you using a Microsoft Outlook calendar? If so, perhaps start adding future meetings in but setting them to “private,” so if this oaf continues to calendar surf he won’t be able to see the details?
Signing up to training without informing you - I’d tell this pillock they need to let you know/ask. Are they even signing up to things that are relevant? We had a case in our own team once where someone was doing this and a lot of the courses she was signing up for weren’t relevant and she also forgot to attend several, which caused headaches too.
Sorry I’m busy when you ask to speak to them -unacceptable. You’re the manager and asking to speak to them is not an unreasonable request.They should be available when you ask.
Contacting client behind your back and then Inviting himself to the meeting with the client - rude, not something he was asked to do and then it transpires he’s wasting time. Ask to not do this again.
If this person is in probation, act quickly and use the options. You could justifiably have a conversation about these issues, set expectations and consider using the option of extending probation due to areas requiring improvement. Ultimately if they’re not getting the tasks assigned done quickly enough and are procrastinating, “being busy,” doing other crud, that’s not acceptable.
I think you could justifiably cite the “I’m busy” when you’ve asked to speak to them and the whole going to the other manager as communication and conduct issues. It’s rude!
If they’re outside of probation, have a look at your own organisation’s performance management policy. If it’s like all the ones I’ve worked with there’s usually an informal stage. You could potentially explore this.
Think you need to set expectations, clarify what you want of them in terms of improvement, timescales for when they need to achieve these by and if they are still causing issues, potentially move on to more formal action.
Hope this helps.