cold shoulder

give the cold shoulder AND turn a cold shoulder to sb (be intentionally ignored or treated in an unfriendly way ) — оказать холодный приём, демонстративно игнорировать

Example 1: I've been getting the cold shoulder every time I go near her. — Она меня просто демонстративно не замечает/не отличает меня от стенки.

Example 2: The office staff gave me the cold shoulder when I did not go to the going away party.— ... отнеслись ко мне подчёркнуто холодно...

Example 3: The membership committee turned a cold shoulder to my request. — ...проигнорировали мою просьбу.

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It is often said that this is from the idea of offering or being given a dish of cold shoulder of mutton left over from a previous meal, interpreted as a sign that the recipient was an unfavoured visitor. However, this is highly unlikely.

The sudden popularity of the expression from the 1820s on, and the total absence of it in literature before Sir Walter Scott used it, strongly suggests that he either invented it or he popularised a saying that beforehand had been uncommon.

It also seems likely that the expression never referred to meat. It is more probable that the cold shoulder was always a direct reference to that dismissive jerk of one side of the upper body to indicate a studied rejection or indifference. Scott's use of 'tip the cold shoulder' and 'show the cold shoulder' would suggest this is so.

See also
[give a wide berth]

Opp.
[roll out the red carpet]
[оказать почётный приём]