There was a general bustle, a rustling of the women's gowns and shuffling of the men's feet, greatly at variance with that hushed repose which should attend the entrance of the minister.

1 that为指示代词，作定语修饰repose。

2 which引导限制性定语从句，并在从句中作主语。定语从句的理解关键是动词attend的词义。attend在此非常正式的用法，为及物动词，意为： (formal) to happen at the same time as something，to exist with something else, or to happen as a result of it 与...同时发生，与...同时存在，因...而发生。例如：

She dislikes the loss of privacy that attends TV celebrity.她不喜欢当了电视名人后随之而来的没有隐私。

Secondary symptoms usually attend the disease.该病常伴有继发症状。

本句中的entrance不是入口，而是进入、登场。the entrance of the minister意为”部长的到来“。

that hushed repose which should attend the entrance of the minister.

伴随部长的到来而呈现的那种安静。