Getting people on the "dance floor" is always tough. Less than 2% of people online engage and in my opinion, LinkedIn Groups seem to be even more challenging than Facebook Groups because LinkedIn is the business network and people are more cautious about affecting their professional brand online.
The best way to foster engagement is to appeal to emotions: how are you solving their pain? Can you speak to their problems using their language? Can you give them an "a-ha" moment that they hadn't thought of?
You could ask simple questions to your group such as: "Which option works better for you: A or B?". (Include a visual for better reach & exposure)
Not knowing your industry, you could ask the group at large: I need your help. I'm looking to get some deeper insights from __________ (insert role/position here) about ___________ (solution you provide). More specifically, are you challenged with _______ (the problem) and how are you currently handling it?
This way, you can do a deeper dive on what their problems are, how they are handling it, and if your solution fits within this.
Hope this helps.