Yes, either your or your customer will need to purchase an up to 5 developer license pack, possibly more. Your developers must always be licensed. You must also ensure that your customer has their own licenses for any application you develop for them with Sencha Ext JS or Sencha GXT on a work for hire basis (where a third party would own the IP of the application and would require distribution rights).
If your customer is not licensed directly, then they will not have the distribution rights for the application afforded with a license, nor will they be able to update or maintain the application.
Generally, your customer must purchase enough licenses to cover your developers and any of their developers updating or maintaining the application. For example, if you use 6 developers to create the application and your customer will support the application with 3 developers, then they would need to purchase two 5 developer license packs, which would cover all the developers.
Alternatively, if you purchased licenses for your consultancy prior to the development, you can assign them to your customer by notifying Sencha and following any other conditions for an assignment included in the license agreement. So in the same example, if you use 6 developers to create the application and your customer will support the application with 3 developers, you could transfer two 5 developer license packs to your customer if you had already purchased them. If you purchased a 5 pack, you cannot transfer less than the entire 5 pack license.