what is the best solution to increase engagement in the supply side of a marketplace?

You'll need to figure out the WiiFM (What's In It For Me) for the attorneys. If they are not engaging it is because what you are offering is not peaking their interests. I know that's a hard edged answer, but I'd rather say something that may not be easy to hear but is honest than anything else.

Understanding the supply side of your market, the lawyers, what they want, what problem they are solving, and why they want it, is a crucial as understanding the demand side.

Doing an in-depth avatar and customer profile including their why is vital.

Let me know if you'd like to discuss on a deeper level.

Hi
The fact that you have user traction (the questions being asked) is great. So that's a good start. Obviously, you need to get the questioned answered asap, or else you won't have returning users. So, this is what I suggest:
1. Sign-up to your competitors website - see what (if at all) they're doing differently.
2. Contact the lawyers who are listed on your competitors website (assuming you can see their details). If they've signed up there, they should be willing to sign up with you.
3. As Steven mentioned before me, it is crucial that you understand why lawyers aren't signing up. Possible reasons:
a. Legal limitations
b. A long/invasive sign-up process.
c. Not enough profit for them (maybe they see the prices being offered on the home page and get deterred)?
d. They just haven't heard about your website?
I've worked (as a lawyer) with a similar platform before, and they seemed to have a very good work flow.

As a startup/commercial lawyer, I've successfully helped hundreds of startups, so I'm pretty sure that I can help you better understand the problem, and then offer some practical solutions. I would just need to get more information [see the website, what country you work in (different cultures and regulations...), sign-up process etc].
I'm willing to give you a free 15-20 min call to get the information (you can use the below link), and afterwards, if I have anything of value to offer, we can schedule another call.
https://clarity.fm/assafben-david/free-advice
Legal marketplaces are a nice model - good luck!

Advert placement is key to every business growth and social media has made it even more easier lately.
For example, Coca Cola has never stopped advertising their products despite decades of being in the market. Yours won't be any different.
You can extend a call or email for further legal assistance, please.

Wow, demand exceeding supply is better than you think. Engaging attorneys is easy. Book a 1-hour call with me and I will walk you through the steps.