also: がせい
A formal New Year's greeting used primarily in writing, especially on New Year's cards (年賀状). Not typically used in spoken conversation.
Write 'Happy New Year' on a New Year's card.
I wish you a Happy New Year.
賀正 is a short congratulatory phrase written on New Year's cards, while 年賀 refers to the act of New Year's greeting or visiting more generally.
Standard kanji form for New Year's greeting; reading がしょう is the most common.
Alternate reading がせい is less common and may be considered non-standard or archaic in modern usage.
Compound of 賀 (congratulation) and 正 (New Year). The reading がしょう is the standard Sino-Japanese reading; がせい is a less common variant.