Wiktionary
leadoff hitter
n. 1 (context baseball English) The first hitter in the batting order, who faces the first pitch of the game. 2 (context baseball English) The first hitter of any given inning.
Wikipedia
Leadoff hitter
In baseball, a leadoff hitter is a batter who bats first in the lineup. It can also refer to any batter who bats first in an inning.