Is it permissible to delay the slaughter of a vow sheep—pledged after obtaining a certain nationality—and slaughter it along with the sacrificial sheep on the day of Eid al-Adha?

It is not obligatory to fulfill a vow of slaughter unless it is an act of worship (qurbah), such as when the one making the vow stipulates it to be charity or for distributing its meat to the poor. If it is a vow of worship and not restricted to a specific time, then according to the majority of scholars, it is not obligatory to fulfill it immediately. Therefore, it is permissible to delay it until the day of Eid, though fulfilling it sooner is better.