I stumbled upon a bunch of example sentences at YouDao wherein 追求 is used as a noun:
I'm skeptical. I looked it up in 现代汉语词典, and it doesn't list 追求 as a noun, and my dictionaries in Pleco didn't list it either. But there's more than one example with 追求 being used as a noun, so maybe it's possible.
Question: Can 追求 function as a noun?
In any case, it seems better to use 目标, 任务, 使命, etc.