Scenarios with multiple pseudoscalars are interesting as they usually tend to provide a framework to naturally realize a light axion with a large decay constant which has rich applications in cosmology, especially in the context of inflation and light dark matter physics. On the other hand, from a particle physics perspective, this facilitates a solution to the strong CP problem with a low Peccei-Quinn symmetry breaking scale. One such realization is afforded within the framework of the clockwork mechanism where the axion can have suppressed couplings with the gluons or photons while its companion axion-like particles (ALPs) have relatively unsuppressed couplings, thereby facilitating detectability. We study a minimal clockwork model for the QCD axion invoking a KSVZ-like setup and examine the visibility of its unique multi-ALP $(a_n)$ signature at the LHC, the most sensitive channel being $p p \to a_n \, (+ \, {\rm additional \, jets})$ followed by $a_n \to γγ$. In congruence with the astrophysical and cosmological bounds for the axion, a striking feature emerges for the case of light ALPs $(m \sim \mathcal{O}(10 \, {\rm GeV}))$ wherein the mass-splittings among the former are so small that the signal profile mimics that of a single broad resonance, or an $axion$ $iceberg$. The scenario is found to be imminently testable by the end of LHC's Run 3 phase for an integrated luminosity of $\sim 300 {\rm \, fb^{-1}}$. A larger average ALP mass, on the other hand, results in multiple closely-spaced peaks with a characteristic signal profile, and would be expected to be seen at the forthcoming HL-LHC. Possible additional signals are also listed.

26 pages, 17 figures. Revised abstract and introduction, improved discussion on the interpretation of signal profiles and on topological defects, updated references; results and conclusions unchanged. Version (with a modified title) accepted in PRD