Redmond was arrested on Tuesday when police found heroin and marijuana in his car after stopping the 26-year-old for a traffic violation.
Authorities later searched Redmond's apartment and found a handgun, which is barred under the terms of his probation for a separate 2009 drug arrest.
Redmond appeared in front of a judge on Thursday to enter a not guilty plea and is to remain behind bars prior to a probation violation hearing on August 24.
His half-sister Tatum thanked her Twitter followers for their support following Redmond's latest arrest, adding that the court hearing went as the family "expected".
Two separate narcotics charges against Redmond were dropped last summer after he completed a stint in a drug diversion programme.
Redmond's half-brother Griffin was hospitalised following a car accident also on Tuesday, but was later released when doctors deemed he was in stable condition.