It is obvious that you have to convince a client with your suggestion. Anyway, I don't think it's so difficult to adapt a web or company CI to a UI design for an application.
Here are some considerations that may be useful, the main focus is to see everything in a positive way:
I would completely avoid doing a design that has nothing in common with the current corporate image. Good or bad is the design they have chosen for their company, and proposing a completely renewed image for their mobile application can even be offensive. In fact, you are giving to your client a perfect reason to not accept your new design.
Making a design adapted to the current corporate image is not an impediment. Instead of seeing it as an obstacle, being a good graphic designer you should see it as a starting point:
Study how far the limitations of the current corporate image can get
What elements of the current ones you can eliminate
What elements of the current ones you can modify
What are the new graphic elements that you will incorporate
At the end of your design you can make a visual list of what the
incorporations and adaptations have been made. With this you could
make a perfect emphasis on the magnificent graphic opportunities
their current corporate image has offered you for the new design.
Particularly, I would avoid stating the omissions, even if you see and know them. Unless they have a good conceptual and graphic reasoning you can demonstrate.
If in spite of this you continue thinking that the new design must omit completely the current graphic guidelines, you can use some resources as:
- Show existing examples of corporate images with a web design CI and a
different graphic style for their mobile applications. There are many, in fact
most of the big multinational brands do it that way: the big sports or car brands. In many cases they only have the logo as a
- If it's a design proposal and having enough time, you could present a couple of options, one faithfully adapted to the actual CI and another relatively free.