If you make or enforce a rule, but you break it one time because of a special situation, you're "making an exception" for that person.

For example, if a teacher has a rule that homework has to be submitted by a certain date, he can "make an exception" for a certain student whose computer broke. 

Use "for ___" to indicate theperson who is allowed to break the rule:

I don't usually give my number out to people I've just met, but for you I'll make an exception.