Possible Clues:

• Some A.L. sluggers
• Players who only bat, briefly
• They don't play the field: Abbr
• Org. that includes the TSA
• Dept. that includes the TSA
• A.L. lineup fixtures
• Some A.L.'ers
• N.L. teams usually don't use them
• They're all hit and no field, for short
• Some AL batters