The term 'private law' refers to

Legal arrangements that people or institutions enter into voluntarily, such as by signing a contract.

Laws that pertain to privacy rights, whether that right is held by an individual or an institutions.

Contractual relationships that are protected by non$-$disclosure agreements $($NDAs$),$ so the nature of them cannot be divulged to outsiders.

Federal constitutional protections against state interference in one's private life.