E175 Captain reported a momentary stick shaker while responding to an RA event during initial climb. The Captain recovered from the stick shaker and after confirming the flight was clear of conflict; rejoined the departure procedure.

Narrative

Departed on Runway XX in ZZZ on the ZZZZZ Departure procedure; we were handed off to ZZZ Departure and checked in with them. ZZZ [TRACON] advised us of traffic ahead that was maneuvering/holding at or around 4;600 ft. and that they were not talking to the traffic. I was unable to make visual contact with the traffic and as we started the right climbing turn on the departure procedure; we received a TA. I attempted to visually acquire traffic however was unable to visually see the traffic. Immediately after the TA; while still in the right-hand climbing turn; we received a CLIMB RA. I increased the pitch to follow the RA and during the pitch increase we received a stick shaker that lasted approximately 2 seconds. I slowly lowered the nose to recover from stick shaker. At this point; I still did not have traffic so continued with the CLIMB RA. Once we received the 'CLEAR OF CONFLICT' aural alert I then established normal climb and continued the right turn back to rejoin the departure procedure.At the initial RA alert; the FO (First Officer) did notify ATC that we received a RA and that we were maneuvering due to the RA. After normal flight was established; we contacted ATC to let them know that we were clear of traffic; and they then cleared us left turn direct to ZZZZZ1. Autothrottles were engaged before takeoff and autopilot was off during the departure and not engaged until clear of conflict. Weather at the time of departure was VMC and we remained in VMC during the TA and RA.