When Fort Pleasent at Pine Bluff was abandoned in late July 1863 Hardy's Regiment was attached to Frost Missouri Infantry Brigade and proceeded with them to the defences of Little Rock.
Hardy's Regiment remained with Frost Brigade until after the evacuation of Little Rock September, 1863. Appearently they remained with Frost Brigade until the Army was reorganized after that. My Guess would be that they were attached to Tappens Brigade once Tappens rejoined the Army in Arkansas.
As a point of information Hardy's Regiment was engaged at the Battle of Jenkins Ferry order of Battle as an independent unit as the 19th & 24th Arkansas Infantry, Which actually was its "Official" title.
It was originally called Dawson Regiment 19th/24th Arkansas in it reorganization at Camp White Sulphur Springs in February 1863, until Col Dawson resigned and Lt Col Hardy took command. It was referred to most commonly as Hardy's Regiment to keep from being confused with the 19th and 24th Arkansas Infantry in the Army of Tennessee. Who where the men that had been captured at Arkansas Post and exchanged at City Point, Virginia.