New Year's greetings; New Year's call; New Year's gift
Refers to the act of visiting or sending greetings at the New Year, and by extension the gift given on such an occasion. Often used in compounds like 年賀状 (New Year's card).
I visited relatives' houses to give New Year's greetings.
I bring sweets as a New Year's gift.
I gave New Year's greetings to my neighbor.
On New Year's Day, I paid a New Year's call to my former teacher's home.
We exchanged New Year's greetings with friends.