From Longman Dictionary of Contemporary Englishcause/kick up/make etc a stinkcause/kick up/make etc a stinkCOMPLAINto complain very strongly Activists have raised a stink about the shipments of nuclear waste. → stink
Examples from the Corpus
cause/kick up/make etc a stink• It's for your protection, so that you have the union behind you if Mellowes kicks up a stink.• It's financial clout that counts or, failing that, kicking up a stink.• It will still contain plenty of business and mortgage borrowers to kick up a stink about base rates. 