There are some approaches to buy a new house while taking out a
reverse mortgage. You can buy the new house with a mortgage small enough that it can be paid off with the proceeds of the reverse mortgage. Another way is to pay all-cash for the house, then reverse mortgage it as before. The other way is to buy the house and take out the reverse mortgage in one transaction. These will be considered in turn.
A reverse mortgage is a loan against your home that you don't have to replay as long as you live there. In a regular or so-call forward mortgage, your monthly loan repayments make your debt go down over time until you've paid it all off. Meanwhile, your equity is rising as you repay your mortgage and as your property value appreciates.