For the closet itself, the issue is likely condensation from the temperature difference between your air-conditioned room and the humid exterior wall. Wipe down all interior surfaces with a vinegar or diluted bleach solution to kill existing growth. Then, improve air circulation by leaving the closet door ajar occasionally and using a moisture absorber like silica gel. Avoid storing clothes in plastic, which traps moisture; use breathable cotton bags instead.

Long-term, consider having a professional assess the wall for insulation issues. In many Dubai apartments, the constant AC use creates cold spots on outer walls where moisture condenses, creating a recurring mold habitat. A thermal imaging inspection can identify these cold spots, and solutions may include improving wall insulation or adjusting AC airflow to minimize temperature differentials. For persistent dampness smells, a mold test can identify if the growth is within the wall cavity, which would require professional remediation.