We report the measurement of e+e-→Ds+Ds2∗(2573)-+c.c. via initial-state radiation using a data sample of an integrated luminosity of 921.9 fb-1 collected with the Belle detector at the γ(4S) and nearby. We find evidence for an enhancement with a 3.4σ significance in the invariant mass of Ds+Ds2∗(2573)-+c.c. The measured mass and width are (4619.8-8.0+8.9(stat.)±2.3(syst.)) MeV/c2 and (47.0-14.8+31.3(stat.)±4.6(syst.)) MeV, respectively. The mass, width, and quantum numbers of this enhancement are consistent with the charmoniumlike state at 4626 MeV/c2 recently reported by Belle in e+e-→Ds+Ds1(2536)-+c.c. The product of the e+e-→Ds+Ds2∗(2573)-+c.c. cross section and the branching fraction of Ds2∗(2573)-→D¯0K- is measured from Ds+Ds2∗(2573)- threshold to 5.6 GeV.