1
general::
Phrase(s): put in a good word (for someone)
Fig. to say something (to someone) in support of someone else. • I hope you get the job. I’ll put in a good word for you. • Yes, I want the job. If you see the boss, please put in a good word.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Make a supportive remark or favorable recommendation. For example, Please put in a good word for me with the supervisor, or When you see her, put in a good word for the department. The use of good word for a laudatory utterance dates from about 1200.
American Heritage Idioms