Airports Authority of India
You had not mentioned whether you will be handling Internal or Overseas recruitment. If Overseas recruitment then Yes, definitely you need a license from Indian Government. All Overseas recruitment firm needs to get permission from Central Government. If internal recruitment then - you can simply register your company. Better you contact a CA he will be fully aware of these procedures.
I went through your website as well. Looks like we both are in the same business. We are only into overseas recruitment. Predominantly our clients are from Gulf Countries. Does greenhouse recruit for local market or even overseas?