か is always KA Sometimes が on the other hand can change sound. It can be pronounced both GA or NGA depending on level of formality and position within the sentence.

I mean - it's understandable. I would have said "What would you like to do that you have never done before?" Or something along the lines of: "If you could choose one thing you would like to do that you have never tried before then what would it be?"

If you want to keep that sentence it should be: "Your business will become better with the mutual trust OF your cooperative partner". On the other hand, I personally think the whole sentence sounds a bit odd. Maybe something like: If you are able to build up trust between you and your business partner, it will be beneficial to you in the long run.