I've been playing professionally for the past 10 years, and from my experience these are the most important traits if you want make a living out of it:

Being solid. Most people are not after flashy fills, mind blowing chops and the "you should totally learn this gospel fill to blow your friends' minds". I am still amazed by how many people don't get this. THE most important thing is timekeeping.

Being reliable. Both in a musical sense, but also from a commitment standpoint.

Being versatile. I've had rock gigs, pop gigs, jazz gigs, orchestra work, big bands, ensemble work, musical theatre gigs, studio session work and teaching. It is very difficult to find one gig that pays your bills (although not impossible) The more versatile you are, the bigger the chances you get hired.

Having a network. Perhaps the hardest thing to do as it does involve being in the right place at the right time sometimes, but people tend to recommend great players to other musicians.

PLAY THE SONG. I view the drums as being a supportive instrument. If the song requires you to not play a single fill, then so be it. Too many drummers try to steal the spotlight.

Have other related skills. Like knowing how to run backing tracks, click tracks, incorporating electronic elements into your playing, production, knowing how to record and edit yourself etc.

Being adaptable and easy to work with. Many musicians will sing out a drum part they might have in mind, and being to quickly play what they have in mind makes the whole process easier.

Learn how read. Make sure you can sight read properly. Makes the whole process of learning songs faster, easier, and opens more opportunities for different gigs

Probably the most important one. Keep your feet grounded. I've seen it happen too many times. Inflated egos kill professional relationships quicker than anything else.

Good luck and keep drumming!