Let start of by correcting some of misunderstandings. You don’t get a MD in cardiology. You get a MD, then you do 3- 7 of residency to become a specialist, then another 1-5 years of fellowship to become a sub-specialist. Cardiology is a sub-specialty that requires a 3 year IM residency followed by a 3 year cardiology fellowship.
So that 4 years of med school followed by 6 years of residency & fellowship (where you’re not especially well paid and med school loans are busily compounding interest), plus another 2 years to earn a MBA (on your own dime). You’re talking about 12 years of post college training before you can even start your “side hustle.”
Residents and fellows will simply not have any free time to consult. (Plus it’s a contract violation that can get an individual fired. And fired means you may not qualify for a medical license and won’t be able to work as a physician. And even if you can get a medical license, not finishing residency means you’re only job options are wound care at nursing homes, an urgent care doc in a box, prison doctor, or doing physicals for insurance companies. Because no specialty board certification means neither medicare nor private insurance companies will reimburse you for services rendered.)
It depends on the terms of their employment contract.
Most doctors do not work directly for hospitals–outside of a few academic faculty. Doctors may work for a large group practice/HMO–like Kaiser where they are employee owners. Or they may work for a democratic, independent small group practice (where after a trial period of 2-5 years as a contracted junior member they buy into the practice and become part owners) who contract their services to a particular hospital or group of hospitals, They work as direct salaried employees for a healthcare corporation which owns the hospital or a group of hospitals. They work as contract employees for healthcare corporation that sells their services to a hospital or group of hospitals. Or they can be a locum tenens (temporary) employee for a healthcare corporation who in turns sells their services to a hospital or clinic. Or they can be tenured faculty at an academic hospital associated with a medical school.
If your contract include productivity goals (and almost all of them do), then you may not have the time or flexibility to take on outside work.
Consulting for clinical trial and drug development typically is more common for academic faculty at major university hospitals. And drug development is almost solely the purview of MD/PhDs at academic hospitals. But while you may earn some consulting $$$, academic physicians have significantly lower salaries than do privately employed physicians.
I worked for a small non-profit medical research organization that, among other things, ran clinical trials for pharmaceutical companies. We employed a few doctors (probably 3 or 4) who did nothing but oversee clinical trails, but most of the employees were PhDs, MD/PhDs or DVM/PhDs who did full time basic medical research including drug development.