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Longman Dictionary of Contemporary English
paternity leave
noun
EXAMPLES FROM CORPUS
▪ But I was not surprised that Sam zoomed in on paternity leave right away.
▪ Father friendliness can not be reduced to a company having a paternity leave policy, paid or unpaid, on the books.
▪ Fathers are allowed two days off as paid paternity leave.
▪ I hereby confirm that your request for 5 days paternity leave has been granted.
▪ So why does paternity leave continue to serve as the barometer of social change for the media?
▪ Still, only 11 percent availed themselves of the official paternity leave policy.
▪ The audience gave a warm welcome to the father of four, fresh from paternity leave.
▪ Tom went off on paternity leave and his secretary organised a whip-round to send a card and a gift.
Wiktionary
paternity leave

n. A leave of absence from a job for a father to care of a baby.

Wikipedia
Paternity Leave (film)

Paternity Leave is a 2015 romantic comedy film directed by Matt Riddlehoover. The film stars Jacob York, Charlie David, and Chris Salvatore. Principal photography of the film began on September 1, 2014 in Nashville, Tennessee. It made its world premiere at the Nashville Film Festival on April 19th, 2015.