Moonlighting or second jobs are generally not ruled out by contracts of employment which is what you are referring to I think as you would be still contracted to your present employer and attempting to start a poistion with a second. This happens a lot and many people have two incomes. However, if you are trying to start with a rival consulting firm I would strongl;y advise against it for a couple of reasons; firstly, it is un-professional and you run a risk of transgressing any confidentiality clauses in your contract which your current employer would take note of, and secondly, you may later need to rely on references from current employer and you don't want a black mark being forwarded to your new employer.Your choice of course, but my advice, enjoy the paid holiday and ask your new employer to wait a bit longer. I'm sure they will.