You might as well ask "How long is a piece of string?" - everything depends on the local geology.
There are thousands of quarries that have been developed for cragging. But there must be a great many more that will never be suitable.
The rock in your picture doesn't look very promising, to be frank, so you might want to do some initial research before committing to the project.
You should discover whether the rock being quarried for building stone or for aggregate. If it was an aggregate quarry you are almost certainly wasting your time.
Is there any similar rock in the vicinity that is climbable and gives you cause for optimism?
If you can find a local geologist, they might be able to advise on the suitability of the rock type.
Arranging legal access
If things still look promising the next step, obviously, is to get permission from the land-owner. Depending on your local laws, this might not be straightforward if there are any issues with liability. Many climbing clubs have access officers who might be able to help.
Suck it and see
If you do get permission you will realistically just have to suck it and see. But the dangers of loose rock are very real so take every precaution. Don't be going there after frost or heavy rain. Do abseil inspections if there are safe belays at the top (and if there are no safe belays, is this really an area where you want to be climbing?). Even after initial cleaning you might want to top-rope the first few routes until you gain full confidence in the rock.
Putting up new routes is fun, but please do be prudent and don't take excessive risks. It's possible that you've stumbled on a hidden gem. But it's much more likely that there are good reasons why this quarry has never been developed!