Your university should have an office that manages environmental and chemical safety issues. You should contact them. The rules and regulations are likely to be different in different countries but you need at a minimum to be compliant with the rules for your university and country.

according to FDA guidelines wear appropriate PPE (nitrile gloves, goggles, lab coat) and work in a certified fume hood. Neutralize the mercury using sulfur powder or sodium thiosulfate then solidify the agar and place it in a leak-proof, mercury-resistant container labeled as hazardous waste. Follow FDA and EPA regulations by disposing of the waste through an approved hazardous waste management service ensuring it is never discarded in regular trash or drains and maintain accurate records of waste handling and disposal to comply with regulatory requirements.

Thank you very much Laila for your response. This is very helpful.