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(1) Subject to Subsections (2) and (3), custom is adopted, and shall be applied and enforced, as part of the underlying law.
(2) Subsection (1) does not apply in respect of any custom that is, and to the extent that it is, inconsistent with a Constitutional Law or a statute, or repugnant to the general principles of humanity.
… (Schedule 2.1)

(1) This Constitution and the Organic Laws are the Supreme Law of Papua New Guinea, and, subject to Section 10 (construction of written laws) all acts (whether legislative, executive or judicial) that are inconsistent with them are, to the extent of the inconsistency, invalid and ineffective.
(2) The provisions of this Constitution and of the Organic Laws are self-executing to the fullest extent that their respective natures and subject-matters permit. (Sec. 11)

WE HEREBY DECLARE that all persons in our country have the following basic obligations to themselves and their descendants, to each other, and to the Nation:-
(a) to respect, and to act in the spirit of, this Constitution;
... (Preamble, Basic Social Obligations)

(1) Subject to this Part, the principles and rules that formed, immediately before Independence Day, the principles and rules of common law and equity in England are adopted, and shall be applied and enforced, as part of the underlying law, except if, and to the extent that-
(a) they are inconsistent with a Constitutional Law or a statute; or
… (Schedule 2.2)