High entropy alloys (HEAs) have been considered as one of the potential structural material candidates for fourth-generation nuclear reactors and fusion reactors due to their excellent irradiation resistance. Current studies have shown that the chemical short-range order (CSRO) usually exists in HEAs, which has a significant effect on the mechanical properties and irradiation resistance of HEAs. Refractory high entropy alloys (RHEAs), as a new class of HEAs have better mechanical properties at high temperatures than face-centered cubic (FCC) HEAs, and therefore have better prospects of application in the nuclear field. In this study, CSRO and its effect on the irradiation resistance of HfNbTaTiZr are analyzed via molecular dynamics (MD) and Monte Carlo (MC). The primary cascade simulations, multi-cascade simulations and surface bombardment simulations are carried out to simulate the generation and accumulation of irradiation damage. The results of the primary cascade simulations and surface bombardment simulations of CSRO models show that the presence of CSRO induces cascade splitting into subcascades. The presence of subcascades reduces the thermal peak enhancement effect and thus lowers the recombination rate of Frenkel pairs (FPs) in the damage zone when FPs concentrations are low. However, the creation of subcascades increases the size of the damage zone caused by the cascade. Thus, when the concentrations of FPs are high, the larger area of damage zone allows more of the already existing FPs to be included, thus promoting their recombination, i.e., impedes their accumulation when concentrations are high. These subcascades lower the recombination of FPs at low FPs concentrations but inhibit their accumulation at high FPs concentrations. The presence of CSRO is also beneficial in inhibiting the growth of point defect clusters, which further improves the resistance of HfNbTaTiZr to dislocation generation. Furthermore, the presence of CSRO facilitates the irradiation-induced phase transition. But it is found that HfNbTaTiZr shows suppression of HCP cluster growth. And the tendency to break down large HCP clusters into smaller ones is demonstrated in the CSRO model. From our calculations we also find that the irradiation-induced HCP atoms have a higher potential energy relative to the matrix. The potential energy difference between those energetic HCP atoms and the matrix can lead to generating a great number of insurmountable barriers pervading the matrix and largely suppressing the long-term mobility of FPs, thus limiting their aggregation and growth into clusters.