Date: 201706
Local time of day: 1201-1800
Location: AUS.TRACON, TX
Light: Daylight
Aircraft: Medium Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class E AUS
ATC / advisory: TRACON AUS
Second aircraft: Small Transport; Low Wing; 2 Turboprop Eng
Reporter organization: Government
Reporter function: Departure; Approach
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Workload; Distraction; Situational Awareness
Second reporter function: Enroute
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic
Contributing factors: Chart Or Publication; Airspace Structure; Human Factors; Company Policy; Procedure; Manuals
Primary problem: Manuals

Narrative: I was working Radar. Traffic was steadily increasing; which always creates more coordination between facilities. I cleared Aircraft Y direct and had them contact Center as that sector had accepted the automated handoff. Shortly thereafter; I received the handoff on Aircraft X descending via the RNAV Arrival. The aircraft was at 16700 feet. I thought Center was going to climb Aircraft Y per the LOA (Letter of Agreement) but apparently that had not taken place yet.I went to Aircraft X and realized they were descending into Aircraft Y that was still level at 12000 feet northeast bound. I issued a left turn to heading 130 degrees and did not issue an altitude. Aircraft X was slow in reply but appeared to be turning but separation appeared to have been lost already. Aircraft X then replied they were responding to a TCAS and climbing. At that time they no longer appeared to be in a left turn but more like 170 degrees. Aircraft X advised me they would file a report and wanted me to provide them with the tail number of the other aircraft. I supplied them with a phone number to the watch supervisor desk. As far as I know; they never called the facility. I am told the closest proximity between the two aircraft was 1.42 miles and 900 feet vertical.Recommend better Staffing on each shift. There was no one available to work the assist position; so Arrival Data realizing the situation and the amount of traffic; left the data position and sat next to me to help with coordination and the extra set of eyes. But he did not catch the impending situation nor did I. There are many days that we have to work combined positions due to the poor staffing here.We have two other positions available to reduce workload; yet we do not have a body to put in the position. May not sound like much but there are several days each month where we have a total count of 1500-1800 operations and we do it with just 3 sectors. A place like the Center works 2500-3000 operations daily but do it with 8-10 sectors. Do the math; staffing is deplorable and services have to be denied or the controllers become stretched so thin that things like this happen constantly. It is only getting worse and morale is getting worse as well. I do not know where the Supervisor was during this; but I believe he was in the radar room. After it happened I reported the event to them. It is my fault; no one else's. I had other options and will exercise them in the future; like keeping both aircraft on my frequency and not depending on the receiving controller to climb the departure out of the arrivals way. We have pretty much gone stripless so I did not know where the aircraft was going until questioning the Aircraft Y. Probably not a great idea. Maybe create a departure procedure for aircraft departing the secondary airports that will ensure separation from the busy arrival procedures. We do not have RNAV departures; because apparently; the airlines do not want them? We also need to stop the excessive coordination with Center and other facilitates and follow the LOAs. Some days; Center coordinates every airplane. Tell them to realize; if you clear aircraft to the same fix; they will get there and then they ask Approach to bail them out with stacks over fixes; or headings other than the Letter of Agreement; etc.


Second narrative: Aircraft X Was on an RNAV Arrival from the north. I switched Aircraft X to Approach. Aircraft Y checked on at 11;700 feet climbing to 12;000 feet. Aircraft Y was on a departure route from Approach. At this time Aircraft X was around 14;500 feet. I gave Aircraft Y the altimeter and told the pilot that he would climb in a couple of minutes for traffic. Aircraft X responded to a RA at 12;600 feet and climbed back to 13;000 feet. When the aircraft were clear I climbed Aircraft Y to 15;000 feet which was his requested altitude.According to the Center/TRACON Letter of Agreement the Transfer of Control Point(TCP) will be the lateral limits of Approach Control core airspace and the shelf as depicted. It states Approach Control must provide separation between departing aircraft and between departures; over flights; and all arriving aircraft which have reached the TCP. The loss of separation happened between 12;000 and 12;600 feet about 5 miles south of the TCP.


Synopsis: ZHU Center Controller and AUS TRACON Controller reported two aircraft conflicted with each other due to a different interpretation of their responsibilities according to the LOA between the facilities.