The phrase "begs an answer" has become quite commonly used in the last few years (perhaps decades) both in print and in speech. It is used to indicate a "request" for an answer from the party who has the ability to provide the information that will answer the question. It connotes that the need for an answer is obvious.
It is most likely a derivative of the phrase "begs the question" which in informal speech generally means "raises the question" in a situation where a point or statement has been made that automatically leads to the need for additional information. It connotes that the need for another question and answer is obvious.
The meaning of the phrase "begs the question" as discussed here is a modern corruption of its meaning in formal logic.
There is a brief discussion of the phrase at the link provided below.