If you are talking about the license then it applies on the server level but not on the system profile.
If you are talking about the agent switching between Classic Agent and the AppMon Agent then you will have to restart the your application and the affected Agents.
Have you copied the agent group properties from one system profile to another system profile say from D4 to D7 and you want to see the monitoring data on D7 system profile. can you clarify here bit.
If you have done above method, you need to remove the agent group from the D4 and restart the application services in order to reflect the agents on the System profile D7. As the agents are already reporting to the server on system profile D4, so you need this step.
If this is not the case, then there is no need for restart.
If you want to check the Dynatrace AppMon licenses, you can verify on
Client --> settings --> Server Settings --> License --> Information (Tab)
This is how it looks
Comment if you are looking for some other details.