1 - Be honest
Be clear with the customer on what the unknown is. Gather what information you can find:
- any documentation on the process and timelines
- any information based on experience with some level of confidence in the source (for example, having done it before within the company is better than an answer in a forum, but an upvoted answer in a StackExchange is probably better then a single voice randomly whining in a blog...)
2 - If possible, change the scope of the work
In many cases, a company will give a customer everything they need to get to the step that is beyond the company's control. For example, my accountant may give me my tax forms, an envelope addressed to the IRS, and the correct paid postage. All I have to do is my part (verify and sign and provide the check) and then I can send in my taxes. And then I can work with the unresponsive big agency (the IRS) myself.
(granted, this is an obsolete example with electronic filing being so reliable)
Rewrite your contracts to give them everything they need, just they way they need it, and let your customer submit for themselves.
3 - Promise exactly your behavior in light of the chaotic factor.
In this instance, it may be:
- deadline by which the request will be made to Apple
- SLA for response in light of any responses from the Apple registration process - for example, turnaround time on any questions or bug fixes.
- expectations of completion of contract regardless of outcome - you can't promise that the third party will do what you want, so what does "completed" mean - is the contract complete after the first accept or reject from Apple? Will you cover the cost of 3 attempts? Is there an additional fee after that? Don't assume success.
4 - Realize that how you mitigate the risk is a factor of your business plan
Different companies will address this differently. Some may develop a core expertise and promise absolute success, because they know that they can achieve it based on their prior experience. But if it's new, you're not likely to be a position where you can promise perfection. Figure out how much time, effort and money you are willing to risk as a company vs. how much risk you expect that the customer will accept.
Customers will shop based on their own decision making process. One customer may make high-risk/low-cost choices, while another holds out for high-cost/low-risk options. A valid way to price the option is to make it a "no worry" process for the customer, but at a phenomenal rate. This really is only viable if you have the knowledge and the talent, since being a high-end, hassle free service also means that you provide consistently awesome communication and general excellence in all parts of the relationship.