Arkansas law doesn't explicitly prohibit felons from working in private clubs. However, the specifics depend heavily on the nature of the felony conviction and the club's own policies. Some clubs may conduct background checks and refuse employment to individuals with certain felony convictions, particularly those related to theft, violence, or alcohol/drug offenses. Others may not have such stringent requirements.
There's no blanket yes or no answer. It's a matter of individual circumstances and the private club's hiring practices.