To be specific, the noun visit takes two semantic arguments, the visitor and the visited entity, as in 'the visit of the Queen to the Prime Minister'.
when used in to pay a visit, the semantic argument, visitor, is realized as the subject of to pay (The Queen paid a visit to the Prime Minister), and cannot be realized at the same time within the NP headed by visit (*The Queen paid a visit of the Lady to the Prime Minister).Paul transmitted the advice to his sister + Peter's advice →Paul transmitted Peter's advice to his sister.