Strictly speaking, as this is a negative, it should be nor rather than or, although the latter is common in spoken English. Don't tell your client, nor his brother means don't tell both.
The sentence is ambiguous in English because "his brother" could be the brother of "he" or the brother of "your client". Let's give them names:
He = Joe
You = Jim
Your client = Jack
His brother= John
When I first read it I thought the brother was the client's brother. Now I've read Steve's answer I realise it's far more complicated, and having English as not your first language can't help. Can you give us more context, poom, without giving away personal details?
There may, possibly, be five people involved . . .
He - the person who asked you not to tell
You - the person who was asked not to tell
Your Client - who was not to be told
His brother - the brother of the Client (if he has one)
His brother - the brother of the person who asked you not to tell
"He asked you not to tell YOUR CLIENT and his brother "
That says to me that it is ok to tell one or the other, but not both.
"HE ASKED YOU NOT TO TELL YOUR CLIENT OR HIS BROTHER?"
I agree with you regarding the "nor": but the above says to me one was asked not to tell either of them.
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