My skip level manager arranges 1:1 every quarter to know if everything is going good, if I need any help from him or if I have any questions. How can I best utilize this time?
I think the core operating principle here is don't talk about the same topics you talk about with your manager. Your skip is operating at a higher altitude, so your goal is to try to see the world through their eyes at this altitude and reverse-engineer questions that tap into this perspective.
All that being said, here's some ideas on what to talk/ask about:
One question I like to ask a skip-level manager: what are the biggest risks to hitting the team goals?
This helps you understand their concerns. Evaluate if you agree with them (and push back if you disagree!), but this also gives you ideas around what projects may be most impactful to help de-risk the goals.
Alex and Rahul definitely touched on the most important topics to tackle during skip level 1:1s! I would only add 1 more potential topic and 1 concern from my side.
Topic: how would you describe a great engineer at my level at my team and what will it be different to be a successful engineer at the next level at my team?
Concern: I recommend being very careful when you complain about your manager to your skip-level.