Measurements of the jet nuclear modification factor in $p$($d$)+A collisions at the LHC and RHIC have unexpectedly indicated that jet yields are suppressed and/or enhanced as a function of event activity (EA). Recent preliminary measurements from STAR in $p$+Au collisions at $\sqrt{s_{{\rm NN}}}= 200$ GeV demonstrate correlations between high-$Q^{2}$ parton scatterings and EA measured at backward (Au-going) rapidities or underlying event (UE) at mid-rapidity. The measurements at STAR disfavor jet quenching as an explanation for the suppression of jet yield observed in high-EA collisions and indicate that these correlations result from the early stages of proton-ion collisions. In these proceedings, we show correlations of backward-rapidity EA with mid-rapidity UE, as well as measurements of EA-dependent modifications to charged hadron spectra and jets. In particular, we present measurements of the UE for various EA selections and discuss its kinematic dependence on jet pseudorapidity and transverse momentum ($p_{\mathrm{T}}$) as a means of examining the correlation between initial hard scatterings and soft processes. We also investigate the EA dependence of high-$p_{{\rm T}}$ hadron and jet properties---including fully corrected jet substructure observables---to study the impact of initial and final state effects.