How to compute the NMR shift in Gaussian09 for only one specific atom in a bigger unit cell?
Short answer, you can't.

It might save a bit of time, but probably not much. The calculation would still need to go through the normal SCF on the entire system to calculate the NMR shifts.

In principal, in evaluating the property calculation, you could save a small amount of time by only computing the one atom, but for most systems, I would think the overall SCF calculation would be vastly greater than computing a few properties.