From Longman Dictionary of Contemporary Englishacquaintanceshipac‧quaint‧ance‧ship /əˈkweɪntənsʃɪp/ noun [uncountable] 1 KNOW somethingyour experience or knowledge of a subject2 KNOW somebodya slight friendship with someone Sheridan had struck up an acquaintanceship with Giles (=had met him and became friendly with him).
Examples from the Corpus
acquaintanceship• Sheridan had struck up an acquaintanceship with the actor-murderer Giles, a slightly bizarre eventuality which might have odd consequences.• Powell married Violet Packenham, sister of Lord Longford, in 1934 after a brief acquaintanceship.• Every two blocks or so he would leave the parade to renew an old acquaintanceship or foment a new one.• Four retakes of my shivering acquaintanceship with the wintry waves were needed.• Presently the Youngs appeared and with smiling acquaintanceship joined Filmer. 