Why can we not execute a stored procedure inside a function when the opposite is possible?
You would need to change your stored procedure to a Function to call it from within a Function.
Or, one way is to use xp_cmdshell to call a batch file where the batch file contains the execute procedure statement. In the function you can call the extended proc.
eg.
Create Function...
EXEC master.sys.xp_cmdshell 'C:\test.bat'
RETURN...
I am in no way saying that this is good practice but am just saying it's a possibility.