Beg leave to do something
Definition 1 of 1
Pro Tip 1/3Polite Request
The phrase suggests a very polite and formal way to ask for permission. 
I beg leave to suggest an alternative solution.
Pro Tip 2/3Old-fashioned
It's an old-fashioned expression not commonly used in everyday modern English. 
I beg leave to retire from the evening's festivities.
Pro Tip 3/3Formal Situations
Best used in very formal contexts such as diplomatic or ceremonial occasions. 
We beg leave to present this gift to your ambassador.