hat in hand - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Also, cap in hand. In a humble manner. For example, They went to her, hat in hand, asking for a change of assignment. This expression alludes to removing one's headgear as a sign of respect and has survived the era of doffing one's hat. [c. 1700]