The driver gets the job from an agent so I'd tend to conclude that the agent is acting as a dispatcher and should be licensed. In any event, basic law dictates that the contract is with the person who pays, in this case the agent.
However, regardless of whether the agent is a DO or not the substantial problem seems to be that the driver must run the meter and may not charge more than the metered fare for each journey. Whether the driver can charge for additional services under a separate contract is probably worthy of consideration, for example he may be acting as a minder while the (using the example above) student is in his care - would a minder have to be PSA licensed?, carer might be a better role?
It seems that the regulations don't accommodate the kind of service under consideration very well. Perhaps an Irish solution is required... something along the lines of the contract requiring the driver to collect a chit from (for example) Rathfarnham and then drive to DAP and collect the student. Then the meter would start in Rathfarnham and the fare displayed wouldn't bother the passenger as it'd be the agent's problem, of course the driver is going to discount the end charge to match the fare agreed?