I moved from a PhD in Astrophysics to an industry job some years ago, so I can share my experience, as well as the experience that a number of my fellow grad students had. This was in the United States, so things may be different in other countries.
The basic idea is that as far as most industry is concerned, a PhD in astronomy/astrophysics is the same as physics, so any job looking for a physics background will do. Jobs looking for a mathematics/statistics background are probably close enough as well, and worth applying to.
Your most marketable skills are your ability to code and do math/statistics while working with data. This is EXTREMELY valuable in industry. Your knowledge of astronomy and physics is likely not very valuable except in some very specific jobs.
Some specific fields that aggressively hire people with PhDs in astronomy in large amounts:
1) Quantitative Finance - The financial world hires a lot of people with PhDs in math/physics/stats to be quants. There are a lot of pros/cons to this field, but it pays well at least.
2) Defense Contractors - This is very much a research type environment. However, this almost always requires that the applicant have US citizenship in the United States in order to obtain security clearance.
3) Software Engineering - A background in coding, data analysis, and mathematics is very desirable. You will likely want to brush up on your programming since scientific programming is not usually software engineering, as well as your statistics.
You can try for more specialized fields like medical imaging, but it is often difficult to compete with the physicists with specialized backgrounds in that specific niche in my experience.