Yes, you can in fact still rent property while under debt review. While it can be tricky in certain situations, this has more to do with reliability and trustworthiness that actual legal guidelines. As an individual under debt review your rentals are not affected, only your level of risk to lenders and your ability to take on new credit.
As a rental is not a credit agreement, there is no reason you cannot take it on. Obviously there are other factors to consider though, like whether you can afford rent and whether the repercussions from missed payment are going to further hurt your payment history. Always ensure that you can cover what you owe, and don’t stretch your finances especially when under debt review already. Learn to budget while you have the money.