What do you think of this idea? - As mentioned in the post, if I give them equity but have a one year cliff and if they don't bring any clients then fire them before one year?
Like, to me it seems you're entering a very problematic relationship, but again, the only info I have is your post. Maybe they are a highly competent, pro-social person that would support you a lot. Based on what you wrote, to me it seems more like they are preying on your desperation to find clients.
On top of that, even if they are a great person, your agreement is very vague and can lead to a lot of bad feelings down the road, on both sides: what if they have completely different expectations than you? You seem to expect them to be your main source of new customers, are you sure they see themselves exactly the same way? And all are your team members on the same page?
I would very strongly advise you to give them only finder's fee on business they bring. If they are not okay with that, then are they going to treat your consultancy as seriously as all the other co-founders you have? If not, I would avoid this entire relationship.