Clyne, off contract from Liverpool, has joined Palace on a short-term deal.
Parish said, "Nathaniel is a fantastic character to have around this squad and we are delighted to secure his services for the upcoming period. He is a first-rate professional, just as he was when I first met him more than a decade ago. His presence and experience will be invaluable."
Having put pen to paper, Clyne said: "I'm a London boy, this is where I grew up. I'm back home and all my family and friends are here. It's surreal being back, enjoying it and hopefully I can just crack on and enjoy my football again."
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