[molf]

You're correct in your intuition that this will affect the business relationship. Would your potential new employer prefer you over the business relationship with your current employer? If no, this is a risk for you which could potentially lose you both job opportunities. In any case you need to discuss this with your potential new employer as soon as you apply.

Some managers are empathic if you are open and honest and you might try disclosing your plans to your current employer somewhat early during the hiring process. This might it less likely for the business relationship with the client (your potential new employer) to sour. Of course, there is the possibility it backfires. Depends on the relationship between you and them.