Check the Refrigerant Level
 

• Low Refrigerant: Air conditioning relies heavily on refrigerant to cool the air. If the levels are low, it may need to be recharged. Low refrigerant could also indicate a leak in the system, which would need a professional's diagnosis and repair.

 
Examine the Air Conditioning Compressor
 

• Compressor Clutch: If the compressor clutch doesn’t engage, it won’t compress the refrigerant to pump it through the system. Listen for clicking noises when the AC is turned on, which is a sign of the compressor engaging.
• Compressor Issues: There might be internal wear or problems with the compressor, which could prevent it from functioning correctly. This might require a mechanic to assess and potentially replace the compressor.

 
Evaluate the Electrical Components
 

• Fuse and Relays: Check for blown fuses or relays associated with the air conditioning system. A blown fuse might prevent power from reaching the compressor or other AC components.
• Wiring Issues: Damaged or loose wiring can affect the operation of the AC system. Inspect wiring harnesses for visible damage and ensure connections are secure.

 
Inspect the AC Condenser
 

• Blockages: Dirt, debris, or damage to the AC condenser can reduce airflow and heat exchange, affecting cooling efficiency. Inspect the condenser, usually located at the front of the vehicle, for any obstructions or damage.

 
Check the Cabin Air Filter
 

• Clogged Filter: A dirty or clogged cabin air filter can restrict airflow through the vents. Replacing the cabin air filter can improve both airflow and the AC system's efficiency.

 
Assess the Blend Door Actuator
 

• Functionality: The blend door controls the mix of hot and cold air. If it's stuck or malfunctioning, it can prevent the system from delivering cold air. This might require replacement if faulty.

 
Consult a Professional
 

• If you've checked the components above and the air conditioning system is still not functioning properly, consulting with a certified mechanic or technician who has the necessary diagnostic tools can provide a more accurate diagnosis and repair.

Each of these factors could potentially contribute to your 2021 Honda Accord's air conditioning system failing to blow cold air. Addressing these areas might help restore the cooling function of your vehicle.