From Longman Dictionary of Contemporary Englishshoot somebody a look/glanceshoot somebody a look/glance (also shoot a glance at somebody)LOOK FOR to look at someone quickly, especially so that other people do not see, to show them how you feelshoot somebody a quick/sharp/warning etc look/glance ‘You’re welcome to stay as long as you like.’ Michelle shot him a furious glance. Jack shot an anxious look at his mother. → shoot
Examples from the Corpus
shoot somebody a look/glance• Nick and I shot a conspiratorial look at each other: this time we would refuse to fight.• The team shot quizzical glances at their new addition but made no move to get rid of him.• He shot me a look brimful of amusement, then drained his cup and sat back in the chair.• She shot a worried glance down to the bottom of the yard.• Joyce shot her a look in which surprise and indignation were nicely fused.• Mandy shot her a look of pure astonishment. 