To garner the laurels, meaning “to collect praise” refers to the ancient practice of awarding crowns of bay laurel leaves to victors in competitions. This tradition of honoring distinction with such a wreath is reflected in the terms Nobel laureate...
If you’ve accomplished something, go ahead and rest on your laurels. Martha traces this idiom back to Ancient Greece, where victors were crowned with a wreath of bay leaves from the bay laurel tree. In the 16th Century, to retire on one’s laurels...

