Easier said than done.
"Deep expertise" is a very subjective term, but it's easy to recognize than define. The feeling of trust that you get from an expert is very concrete. Building that trust in your client takes various forms in various industries. Let's take one of the most common one: Certification.
When do you trust a doctor? When you see an MBBS (in India) stuck next to his name you assume that he/she knows his/her "stuff" when it comes to diseases and the human body at a basic level. We assume that because the Doc has had 4 years (or more) of life dedicated only to that. Certifications and specializations are your calling card when you want to show expertise.
Reference is the other.
Let's continue the thought further. Someone has a heart condition (high cholestrol, or whatever) and you go to a plain vanilla MBBS doctor who says "this is not what I can handle, go check Dr. Abcd, MBBS, MD (Cardio) for this". Off you go to Dr. Abcd because you trust the first doctor's judgement. If Dr. Abcd succeeds in treating you, Dr. MBBS also gets your gratitude.
You get the drift, I assume.
What happens if your industry doesn't have certifications?
- Do something extraordinary !
- Let others know about it.
- Keep raising the bar for yourself.
Taking assignments where your area of expertise is involved helps you to guarantee higher percentage of success. The focus however, should be to get involved in assignments that are not identical and always to push one's comfort zones.