We propose a novel approach to probe new fundamental interactions using isotope shift spectroscopy in atomic clock transitions. As a concrete toy example we focus on the Higgs boson couplings to the building blocks of matter: the electron and the up and down quarks. We show that the attractive Higgs force between nuclei and their bound electrons, which is poorly constrained, might induce effects that are larger than the current experimental sensitivities. More generically, we discuss how new interactions between the electron and the neutrons, mediated via light new degrees of freedom, may lead to measurable nonlinearities in a King plot comparison between isotope shifts of two different transitions. Given state-of-the-art accuracy in frequency comparison, isotope shifts have the potential to be measured with sub-Hz accuracy, thus potentially enabling the improvement of current limits on new fundamental interactions. A candidate atomic system for this measurement requires two different clock transitions and four zero nuclear spin isotopes. We identify several systems that satisfy this requirement and also briefly discuss existing measurements. We consider the size of the effect related to the Higgs force and the requirements for it to produce an observable signal.