If you had to pick one, which attribute or skill have you found is the most important when dealing with clients/customers?

Read through the job description to identify the skills that are required or mentioned frequently. If they are replacing a client services manager those required skills are more than likely what the previous manager lacked.

"I would say the most important skill for a client services manager to have is to ensure client satisfaction. I believe this can be achieved in many different ways. The client services manager needs to be able to understand technical details, must be able to listen (especially to an upset customer) and communicate ways to turn the guest experience around."