There is not an actual term for that time. As a reference, given all the wrong (based on my interpretation of the question) answers, Sampling frequency = rate at which something is sampled = 1 / sampling period.
If the sampling frequency is 100Hz, it means the sampling period is 10ms. So, if the actual act of sampling takes 9ms, and there is 1ms until the next sample, that 1ms is not the sampling period.
What an engineer would term that 1ms time is context dependent. Most won't have a name because there may not be a need to actually talk about that time. For the purposes of filtering or operating upon the sampled values, that datum is useless.
If on the other hand, you need to discuss behavior or properties of your sampler, for example, if you're sampling as fast as possible and the sampling device needs a certain amount of time to "reset" or some other action before it can sample again, it may be called dead time, blank time, or OFF time. There, the term that is chosen conveys information about the sampler's behavior.
So really, the name depends on the purpose of the information you need to convey about the 1ms time.