A321Captain reported receiving a TCAS RA for a VFR aircraft at 10;500 ft.

Narrative

Just prior to the ZZZZZ fix on the ZZZZZ [departure] from ZZZ; we were given climb and maintain 14;000 ft. After climbing out of 10;000 ft. and before the turn to ZZZZZ1; we noticed an aircraft on TCAS just north of ZZZZZ1. As we were just about to turn left on course at ZZZZZ1; while in the climb; we received an RA with CLIMB and INCREASE CLIMB. The FO (First Officer) was PF (Pilot Flying) and he immediately disconnected the autopilot; I turned off the flight directors; and the FO increased the climb on the vertical speed into the green. At the closest point; I remember the target on TCAS being red in color and 200 feet below us while still climbing. No visual contact was made with the conflict aircraft. I notified ATC we were responding to an RA. After the aircraft stated CLEAR of CONFLICT we resumed a normal climb rate and ensured we were back on course. No mention from ATC about the aircraft near that fix. ATC later asked us if the traffic in question was the VFR traffic at 10;500 ft.The aircraft in question may have been a parachute jumping aircraft. The proximity to their location and the departure procedure may have been an issue since climbing via the departure was only issued prior to ZZZZZ. After ZZZZZ we were given climb and maintain higher altitudes on the departure procedure. Had we been instructed to climb via the departure procedure we may have been 'out of the way' of the parachute jumping aircraft. OR had we been given vectors to avoid that area all together may have prevented the RA. Execution of the RA procedure by the PF went well. Maybe having been taken off of the departure route segment and turn away from the VFR traffic may have prevented this aggressive maneuver.