Your client looks worried.
Yes, they agree your new idea is a great idea. But like any change, they’re concerned about risk.
Logically they know nothing ventured, nothing gained. They’re not stupid. They’re uneasy. Telling them over and over to do it will not make them do it. Telling them over and over won’t alleviate uncertainty. It won’t calm their anxiety and stress.
The easiest way for your client to ease any apprehension is to do nothing. If you want to ease uncertainty, lower the barrier to trial. Give them a small taste to they can experience the beginning of change themselves. So they can start to diminish the risk they feel.
You can also reduce uncertainty for them by making things reversible. Let’s say you’ve created an amazing new website. New navigation, new user experience, new paths to purchase. New everything.
Let the client know that if some new element doesn’t work, you can switch it back in seconds.
Evaporate the risk in front of their eyes.