I thought the otherway around
the landlord should pay the agent for renewal agent fee

Contractual Intention from Singapore Law of Contract
Thanks.
The agent didn't sign the contract with the landlord.

According to Singapore Law of Contract http://www.singaporelaw.sg/content/ContractLaw.html#Section1
In the absence of contractual intention, an agreement, even if supported by consideration, cannot be enforced. Whether the parties to an agreement intended to create legally binding relations between them is a question determined by an objective assessment of the relevant facts.

The agent has no contractual intention to such term, the agreement cannot be enforced. It is the same for landlord if the following terms exist:
"If the tenancy is renewed or extended, the landlord should upon the commencement of the commencement of the new or extended tenancy pay to the broker a further commission of one half(1/2) month's revised gross rental........"

即使合同中有说要给中介钱，
但是合同双方只要都认为不给，就可以不给。不可能合同保障第三方，损害合同双方。