Rare-earth intermetallic compounds exhibit rich phenomena induced by the interplay between localized f orbitals and conduction electrons. However, since the energy scale of the crystal-electric-field splitting is only a few millielectronvolts, the nature of the mobile electrons accompanied by collective crystal-electric-field excitations has not been unveiled. Here, we examine the low-energy electronic structures of CeSb through the anomalous magnetostructural transitions below the Néel temperature, ~17 K, termed the 'devil's staircase', using laser angle-resolved photoemission, Raman and neutron scattering spectroscopies. We report another type of electron-boson coupling between mobile electrons and quadrupole crystal-electric-field excitations of the 4f orbitals, which renormalizes the Sb 5p band prominently, yielding a kink at a very low energy (~7 meV). This coupling strength is strong and exhibits anomalous step-like enhancement during the devil's staircase transition, unveiling a new type of quasiparticle, named the 'multipole polaron', comprising a mobile electron dressed with a cloud of the quadrupole crystal-electric-field polarization.