Corporate pilot reported a NMAC during arrival descent and responded to a TCAS Resolution Advisory to avoid the conflict.

Narrative

To the best of my recollection: Day 0 approximately XX:00. Reposition from ZZZ to IAD to pick up pax. Leg 3 of 4/ empty leg. Flying the CAVLR 4 arrival to IAD we were originally given a descend via and then subsequently told to level at 5000 feet. D-ATIS indicated 19C/19L approaches in use. Crew briefed ILS19L and discussed possibility of being assigned 19C. When asked where we were parking by ATC; pilot monitoring (PM) responded with 'Company' and had loaded the ILS 19L. Crew had previously briefed ILS19L and discussed possibility of 19C. Pilot flying (PF) commented 'we're going to Company 1' and we informed ATC. ATC advised us to expect 19C. We were instructed to descend to 4000. PF began the descent to 4000. PM was busy modifying/tuning/briefing the 19C approach and verifying arrival. PF observed the Autopilot initiate capturing the assigned altitude during the shallow descent from 5000 to 4000 while dividing attention between verifying the correct approach/arrival fixes had been loaded by PM. During implementation of this last-minute change; ATC advised crossing traffic at our 10-12 o'clock and requested we expedite to 4000. We responded; 'in sight' and maintained visual separation with the west to eastbound traffic. Noticing the aircraft automation seemed to be capturing the 4000; we subsequently received a TCAS Resolution Advisory and PF complied with RA and leveled at 4000 and advised ATC. The approach to ILS19C was checked and loaded with a quick briefing and the remainder of the approach and landing was uneventful.Potential contributing factors and considerations leading to this event: CALVR 4 STAR descend via and then level off at 5000 with runway changes created an elevated workload dividing PF attention between subsequent descent (and how the automation was responding) and verifying the new approach and arrival. Nominal proficiency/experience with rapidly loading and verifying the new approach at a non-routine high-density airport. While highly experienced; both pilots are low time in type and the aircraft/automation is new to the company fleet.