You can use a Logic App for this if you have it set up with an Integrated Service Environment: https://learn.microsoft.com/en-us/azure/logic-apps/connect-virtual-network-vnet-set-up-single-ip-address
The ISE is setup inside a virtual network, and the network can have a static IP assigned to it.
What may work better for you is an API Gateway. By default they have a static IP that only changes when you do things like delete and recreate the resource. You could further stabilize it using the same method as the logic app- putting inside a virtual network that has it's own static IP. You would set it up exactly like you are describing for your Logic App. Create an API route that reaches out to the third party service. Dynamics would them call the API management instance to retrieve the data.