Indiscreet means lacking caution or carefully thinking before speaking or acting. It refers to someone who is not careful about keeping things private or confidential. Full definition
Perhaps he had been indiscreet in dinner - table discussions with longtime associates in the political wars, and perhaps his somewhat greedy friend William Duer had profited from the information, but Hamilton never intended to «deal out secrets» for anyone's personal gain. (bookbrowse.com)
[8] A lawyer should avoid indiscreet conversations, even with the lawyer's spouse or family, about a client's affairs and should shun any gossip about such things even though the client is not named or otherwise identified. (lso.ca)
Apart altogether from ethical considerations or questions of good taste, indiscreet shop - talk between lawyers, if overheard by third parties able to identify the matter being discussed, could result in prejudice to the client. (lso.ca)