这里的should在虚拟条件句中用以加强假设语气,用"should+do"指将来的情况,当"万一(会)"讲,这句话if省略,should作为情态助动词提前了,所以比较难懂.
原句应该是：It is understood that her cloest advisor will take over as president if she should resign early.
意思是：一旦她提前辞职,她最亲密的顾问就会接替她成为总裁,这也是可以理解的.
类似例句：①Should it rain tomorrow,I should/ would stay at home.万一明天下雨的话,我就待在家里.
②Please call me should you need my help.万一需要我帮助的话,请给我打电话.(此句中should need可用need代替.)
希望我的讲解能帮到你.