It is probably not okay.
While sending a holiday greeting card of you pictured with a celebrity would not (generally) be a problem if the card were just sent to family and friends (because family and friends generally know you well enough to know what your real relationship with the celebrity is), sending the same card to business clients is legally risky.
The photo of you with the celebrity on a holiday business card could (and probably would) make it appear that the celebrity supports or endorses your business, or is connected with your business in some way. If the celebrity does not officially support or endorse your business or does not have a connection with your business, the celebrity could sue you.
The celebrity would not likely sue you for defamation (of course, this could depend on what type of business you have) but the celebrity could likely sue you for misappropriation of their name or likeness. Celebrities' names and images are valuable, are often trademarked, and are protected by publicity right laws. Celebrities are often paid large sums of money for the use of their name and/or image to help in the advertising and promotion of a product, service, or business.
Business holiday cards sent to business clients are a form of business advertising, and you cannot legally use the name or likeness of a celebrity (or any individual) for any advertising purpose without (usually written) consent.
