We present a new fast radio burst (FRB) at 920 MHz discovered during commensal observations conducted with the Australian Square Kilometre Array Pathfinder (ASKAP) as part of the Commensal Real-time ASKAP Fast Transients (CRAFT) survey. FRB 191001 was detected at a dispersion measure (DM) of 506.92(4) pc cm-3 and its measured fluence of 143(15) Jy ms is the highest of the bursts localized to host galaxies by ASKAP to date. The subarcsecond localization of the FRB provided by ASKAP reveals that the burst originated in the outskirts of a highly star-forming spiral in a galaxy pair at redshift z = 0.2340(1). Radio observations show no evidence for a compact persistent radio source associated with the FRB 191001 above a flux density of 15 μJy. However, we detect diffuse synchrotron radio emission from the disk of the host galaxy that we ascribe to ongoing star formation. FRB 191001 was also detected as an image-plane transient in a single 10 s snapshot with a flux density of 19.3 mJy in the low-time-resolution visibilities obtained simultaneously with CRAFT data. The commensal observation facilitated a search for repeating and slowly varying radio emissions 8 hr before and 1 hr after the burst. We found no variable radio emission on timescales ranging from 1 ms to 1.4 hr. We report our upper limits and briefly review FRB progenitor theories in the literature that predict radio afterglows. Our data are still only weakly constraining of any afterglows at the redshift of the FRB. Future commensal observations of more nearby and bright FRBs will potentially provide stronger constraints.