For various professional
Being an expert in your field makes you a professional in your own right. An expert tends to get more jobs and contracts than just an intermediate or beginner in the same filed. Being an expert means you must have put in a lot of work and time to practice and gain experiences and certifications needed for your moving forward. The .EXPERT domain could be used to showcase how good you are at what you do and you are not scared to show that.
For online question and answer website
A forum dedicated to a certain niche or group of people will surely combine both beginners and experts in that field. Using a .EXPERT domain extension for your forum will show that you forum is dedicated to solving problems and helping people navigate that niche or field the forum is dedicated to. Question and answer website also contain two parties, the askers of question and the answerers of questions. Using the .EXPERT domain helps to add a certain level of credibility to whatever is coming from such a question and answer website.
For support pages of various businesses
To correctly solve customer problems and resolve issues speedily and effectively, the support system needs to be handled by experts in the business. So Using the .EXPERT ending for your support page helps to build the confidence people have in your service.