It depends on the company and what the job role is but generally 18+ is required.
If you're solely going to be based within the terminal (such as on a ticket desk or on permanent check in) then it shouldn't be a problem getting a job unless the company has specific rules about that. However, most handling agents don't work this way and PSA staff are trained to do 'everything'. Depending on the airport and handling agent, PSA are required to stand outside on the ramp to supervise passengers embarking/disembarking aircraft. To get an airside pass with the relevant zones to access the ramp you need to be 18 due to various health and safety laws.
I spent two years working airside in the terminal before starting my role as dispatcher, on my 18th birthday