raise (a few) eyebrows - to shock or surprise people.

There were raised eyebrows and coughs of disapproval when the speaker turned up drunk for the lecture.

• have a way with something
• have a weak spot for
• have a weak spot for someone
• have a weak spot for something
• have a whale of a time
• have a word
• have a word in ear
• have a word in someone's ear
• have a word with
• have a word with someone
• have back against the wall
• have back to the wall
• have bags under eyes
• have bags under your eyes
• have bats in the belfry
• have beady eye on
• have beady eye on someone
• have beady eye on something
• have been around
• have been around a bit
• have been in the wars
• have big ears
• have bigger fish to fry
• have blinders on
• have blood on hands