Knight shift measurements probing Fermi surface changes under pressure in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>CeRhIn</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:math>

We report nuclear magnetic resonance (NMR) Knight shift measurements of the In(1) and In(2) sites in CeRhIn$_5$ as a function of pressure. In contrast to the $c$ axis, the in-plane components of the In(1) Knight shift tensor exhibit little to no pressure dependence. These results indicate that the dipolar component of the tensor is strongly suppressed at the In(1) site, while it remains constant with pressure at the In(2) site. We analyze the hyperfine coupling in terms of a tight binding model for the electronic structure, and determine that the pressure dependence of the In(1) shift cannot be explained in terms of changes to the crystal field parameters, but rather can be understood in terms of an increase in the 4f electron content at the Fermi surface. Our results indicate that the hyperfine coupling reflects changes in the electronic structure near a Kondo breakdown quantum critical point.