Wiktionary
vb. (context tennis English) To win a set, or by extension a match, by hold#Verb serve#Noun (winning a game as the server).
Usage examples of "serve out".
And as for Laurent, we took him because we had the opportunity and the Queen said he ought to be brought back to serve out his punishment as a runaway.
He might think she was going to meekly serve out her time as his servant, but Min had no doubts who would end doing what who wanted.
He might think she was going to meekly serve out her time as his servant, but Mm had no doubts who would end doing what who wanted.
In certain shops nothing is vended but the wine of the country, which they are continually brewing, and serve out fresh to their customers at a moderate price.
The elder nobles serve out of tradition, but some seek to break up the kingdom and seize their own territories.
The idea, when Roger asked me to be Vice President, was that I serve out the remaining term and leave government service for good.
If an apprentice is reckoned unfit to serve, it is meet that the Dowayne of his or her House provide a means for them to serve out the terms of their indenture in the time allotted.