Answer
Haridāsa Ṭhākura and Advaita Ācārya were older than Caitanya Mahāprabhu. Thus, we see that Haridāsa Ṭhākura became elderly and eventually left his body in Jagannātha Purī, in the presence of Caitanya Mahāprabhu. He was such an exalted devotee that Caitanya Mahāprabhu personally took his body and danced with it in Jagannātha Purī.
So, Haridāsa Ṭhākura was indeed older than Caitanya Mahāprabhu.