This type of situation happens often in business - especially in travel. Things happen, and we have to be able and willing to be flexible. This can be hard for some people. When you are in a client service role, you have to deal with change from two angles, your own, and that of your customer. How you handle these challenges will directly affect your client’s overall experience.
Being prepared is your best defense against a bad experience with unexpected change. Having a “Plan B” is always a great option. If you cannot be prepared in advance, at least have the knowledge and resources at hand to do what you need to do in the event your client’s airport transfer does not arrive, or their flight is cancelled and they will miss their connection. Your calm approach will be welcome, and contagious.
As they say - stuff happens. Change is inevitable. It’s how we handle it that truly matters.