ARTCC Controller reported having to stop a Tower departure handoff for conflicting Control Tower traffic below the MVA. Controller stated this is a frequent unreported hazard and adding a Tower BRIGHT scope would enhance safety of operations.

Narrative

Aircraft X on ZZZ3 SID Runway X and climbing to 140. Stopped below or MVA but above our polygon for reduced RV abilities when ZZZ radar is turning at 060 to avoid bad situation. Traffic at 065 W/B unknown type; etc. Later determined that this was Aircraft Y talking with Tower 10 east of field over Area. Not sure but suspect bad pilot report that lead to bad Tower assumption to release the Aircraft X to Center and have the Aircraft Y make left traffic which crosses path of Aircraft X to get on downwind for Runway XX. Assumed proximity would have kept these guys apart from Tower since the Area is southeast of actual centerline for Runway X departures?Aircraft X responded to RA and climbed once clear of Aircraft Y. Pilot estimated 900 ft. (our range would probably have little vertical) miss and this is during a very critical point after rotation and while cleaning aircraft; changing frequency in hopefully a timely manner; etc.Training was in progress with transfer CPC-ITI noted flight status unknown because there was only a selection for none but Aircraft Y was talking with ZZZ so unsure if they could have issued traffic call without seeing Aircraft Y and set up aircraft for downwind or base purely on pilot reported positionRecommendation: BRIGHT = safety Daily situations like this go unreported. We are saturated daily and this is slow period. Staff is needed.