Can someone have a career outside of Chess and still compete at a Master level (NM, IM, GM, etc.)?

That was quite a big span

GM Pepe Cuenca has a degree in maths

I’m saying give or take 

in my country Zambia no one plays chess as a day job..all IMs from my country are not professional chess players.. they are rate at 2100 and 2300.the current local champ even draw against ivanchuk rated 2700 in batumi

Short answer:- yes.... 

Wdym compete.. you could become the master ( the main career)by practicing and also do other careers too for the support along with main career

See above...

Currently there's that British GM but I can't remember his name. He's in the 2600s, closer to 2700 I think. 

Somebody on here will know who I'm talking about. I keep thinking his regular job is related to financial stuff for some reason. 

This describes most chess masters, believe it or not.

You can't really earn a living wage from chess competitions alone, unless you're a strong GM who regularly performs well in high-profile events.

Most masters are not strong GMs. They're NMs, CMs, FMs, IMs ... they usually supplement their income by offering private lessons to students, and/or working a completely different job.

Luke Mc Shane

Sammy Reshevsky did.

of course!

     Most players at the NM, CM, and FM levels cannot make a living off of chess. Many such players are young and also students. Some will continue to rise through the ranks of chess players, others will have to spend more of their time on their quotidian work and family activities and will not be able to spend the time necessary to progress further in chess.

     GMs must spend enough time on the game to stay current with the opposition and maintain their ratings that an extensive outside career is impossible. Some GMs reached their level at a young age and continue to play occasionally while pursuing another career. And a few very strong players are strong enough to keep their place at the top level and still pursue other work that would be a full-time career for most people. (Reshevsky making his living as a CPA, Taimanov was also a concert pianist, Botvinnik an electrical engineer, Edward Lasker a math professor, and others.)

Amateur players can be masters as well. Difference between pro and amateur is that the primary source of income for a pro is said activity while the amateur's primary source of income is not in said activity. That's the only difference.

Botvinnik and Vidmar were engineers.
Euwe was a math teacher.
Lasker, Steinitz, Anderssen were a mathematicians.
Capablanca was a diplomat.
Hübner was a professor in Egyptology.
Nunn is a mathematician.
Taimanov was a pianist.
Portisch was a singer.
Tal was a journalist and editor of a chess magazine 64.
Ding is a lawyer.

I would think it might be possible to balance both a full time chess workload and a writing career or something else that you can do on your own time that doesn't require the typical constraints of a mainstream job. Of course, you would have to be a very good writer to bring in enough money to support yourself to a decent extent.

There are only two: naka and smirnov. They are here for pride and only to beat others and not to learn chess

There's an IM from India, who is also the joint head of Chessbase India, Sagar Shah. He completed his C.A degree alongside of playing chess and becoming an IM.