expression, suru verb (special)
apologize for a long silence; express regret for neglecting a friendship
A formal, literary expression used in letters or speeches to apologize for not having been in touch for a long time. Rare in modern conversation.
年賀状の書き出しに「久闊を叙します」と記した。
I began the New Year's card with 'I apologize for my long silence.'
ご無沙汰 is the common, everyday expression for 'long silence' or 'neglecting to stay in touch'. 久闊を叙する is a much more formal, literary alternative.
A Sino-Japanese set phrase combining 久闊 (long separation) and 叙する (to express, to state). The exact historical origin is uncertain, but it follows classical Chinese epistolary conventions.