Date: 201711
Local time of day: 1801-2400
Location: DFW.Airport, TX
Flight conditions: VMC
Light: Daylight
Aircraft: Large Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class B DFW
ATC / advisory: TRACON D10
Second aircraft: Small Transport; Low Wing; 2 Turboprop Eng
Reporter organization: Government
Reporter function: Approach
Reporter qualification: Air Traffic Control Developmental
Human factors: Workload; Communication Breakdown; Situational Awareness
Second reporter function: Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft TA; Automation Aircraft RA; Person Flight Crew; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action; Flight Crew FLC complied w / Automation / Advisory
Contributing factors: Airspace Structure; Human Factors; Procedure
Primary problem: Human Factors

Narrative: Working Arrival Radar. A Tower requests a release from GKY airport; 270 heading and climbing to 3;000. I approve it. The aircraft finally departs five minutes and some number of seconds later; at which point I forgot about the release. I was under the impression that type of coordination is only good for 3 minutes. The aircraft departing climbs westbound into the flight path of the arriving [large transport]. They got about 700 feet vertically and then the [large transport] responded to a TCAS RA.Well; the stale coordination was obviously a factor. But I also will probably not approve any releases climbing to 3;000 in the future. I will only approve climbing to 2;000 at least when I am that busy. Also it wasn't that I was that busy; but the fact that it was three runways worth of arrivals to DFW so I was pushing all my base traffic down ASAP to help the other sector get their traffic down and in.


Second narrative: We were on a 020 heading to intercept the final approach course descending through around 3;600 feet; about 9 DME on the ILS; cleared for a visual approach. The First Officer was flying; with the autopilot on. Approach issued a traffic advisory about traffic ahead; indicating an altitude 3;500 feet; about the same time the TCAS issued a traffic alert. The TCAS showed traffic ahead; and about level. Soon after the TCAS issued a climb RA. The First Officer disconnected the autopilot and followed the RA. I told Approach we were climbing in response to the RA.I saw the traffic as it passed underneath; heading westbound; about 200 feet below. When clear of the RA we resumed the Visual Approach for an uneventful landing. After arrival at the gate I called dispatch and notified them of the TCAS RA and estimated the separation at 200 feet. If we had not had the RA we would have been very close to the aircraft; possibly hitting it. We passed directly over the aircraft; and had we continued descending we would have been at about the same altitude.We were in the Class B airspace; there should not have been any traffic at that altitude which Approach did not know about. All of the altitudes are approximate as I was looking outside most of the time; except when I briefly looked inside when the RA occurred to verify the First Officer was following the RA.


Synopsis: An Approach Controller and air carrier flight crew reported a near mid air collision due to poor ATC coordination on a departure from a satellite airport.