will send a new purchase order/requisition
Если это заказ на закупку/договор-заявка.
Order - если речь о другой организации,
requisition - если внутри одной организации.
https://smallbusiness.chron.com/difference-between-requisition-purchase-order-32609.html
Насчёт send не уверена, зависит от контекста. Если заявка подаётся дистанционно, то почему бы и нет?

Отмела submit a new order сначала, но оно встречается тем не менее.

Anna, we have a word for that: reapply. And we don’t MAKE applications.

The Constitution permits persons, who are citizens of a British Commonwealth country and who have been ordinarily resident in the Falkland Islands for at least seven years, to make application for Falkland Islands status under an Ordinance making provision for the grant of such status.

MAKE APPLICATION = to PETITION, to present a formal petition to a government agency or court system contesting something and petitioning that they do something, as in your example. However, for work, you FILL OUT an application and SUBMIT it.

so you will FILL OUT another application, or better SUBMIT another application, or best: REAPPLY

Подаст новую заявку - не уточняет куда он/она собрались ее подавать

Спасибо, мне всё понадобилось!