Almost everything will drop clear given time, unless it's really abused (starch hazes, polyphenol hazes, etc, can be permanent). Most haze in beer is either from protein, suspended yeast, or from hops, and all will drop with time and cold. Even the haze-craze NEIPAs will drop bright with time unless unscrupulous brewers do something to make them artificially hazy (cough adding flour ie starch haze cough).
In your case, chill haze is typically protein and very, very common, even amongst commercial breweries who don't filter. Good process can reduce it (highly modified malt, good hot break from a proper boil, etc). Finings will help as well (irish moss or whirfloc in the kettle, and then gelatine, biofine, isinglass, brewer's clarex, or any number of other options in the fermenter). Or filtering. Or centrifuge. The latter two not really necessary or practical for the hombrewer (those hombrew-scale filters are mostly sh** anyway and I can't name a single homebrewer who centrifuges).
The trick is for cold side (ie not kettle), fining or filtering always needs to be done COLDER than serving temp. Haze causing particles, especially chill haze-causing proteins, could stay in solution warmer than serving, not be removed by whatever method, and then when you do drop to serving temp, come out of solution and form your haze.
Whirfloc in the kettle, gelatin or isinglass in the fermenter/keg after cold crashing. That's my recommendation. I've heard great things of biofine and brewer's clarex as well, but no direct experience with either.
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