Based on previous studies that support the important role of the N*(2120)D-13 resonance in the gamma p -> K+ A(1520) reaction, we make a re-analysis of this A(1520) photoproduction reaction taking into account the recent CLAS differential cross-section data. In addition to the contact, t-channel (K) over bar exchange, s-channel nucleon pole, and N*(2120) [previously called N*(2080)] resonance contributions, which have been considered in previous works, we also study the u-channel A(1115) hyperon pole term. The latter mechanism has always been ignored in all theoretical analysis, which has mostly relied on the very forward K+ angular LEPS data. It is shown that when the contributions from the N*(2120) resonance and the A(1115) hyperon are taken into account, both the new CLAS and the previous LEPS data can be simultaneously described. We also show that the contribution from the u-channel A(1115) pole term produces an enhancement for large K+ angles, and it becomes more and more relevant as the photon energy increases, being essential to describe the CLAS differential cross sections at backward angles. Furthermore, we find that the new CLAS data also favor the existence of the N*(2120) resonance and that these measurements can be used to further constrain its properties.