ZFW Controller described a pilot deviation event near TXK between an IFR arrival that began a premature descent; and an IFR departure; the arrival issued a downwind entry; 'expect' a visual; but instructed to maintain altitude.

Narrative

Aircraft X was inbound to TXK from TRI. Aircraft X had checked on; had been issued the TXK altimeter; and been asked to advise receipt of the TXK ATIS. Aircraft X did so; then was cleared to 3000 and asked to report TXK in sight. The TXK Tower Controller called for release of Aircraft Y; with routing of TXK..CEW..DTS. Aircraft Y was released; specifying an altitude of 2000 to maintain. This created essentially a nose-to-nose situation; but with vertical separation assured. The departure message came through for Aircraft Y; followed shortly by Aircraft X reporting the airport in sight. Aircraft X was advised that traffic was departing Runway 4; and that the approach clearance would be issued after separation had been achieved. At this time Aircraft X was about 12 miles or so northeast of TXK. The TXK Tower Controller was called; and advised of the plan. Then Aircraft X was cleared to enter right downwind for Runway 4; but no change of altitude was issued. The clearance was given; so as to give the aircraft somewhere to go besides continuing straight to the airport. Aircraft X was expected to maintain 3000 until cleared otherwise. Aircraft Y checked on the frequency out of 1;800 for 2000. Aircraft Y was issued a 010 heading; away from Aircraft X; in order to spend as little time as possible before being able to climb. The altitude of 2000 was restated and a traffic call was begun; when it was noticed that Aircraft X was showing altitude of 2300. When queried; Aircraft X replied that they had taken the clearance to enter right downwind as clearance to descend. It was reiterated that no altitude clearance had been given to Aircraft X; and that they should climb and maintain 3000. By this time; the aircraft were less than two miles apart at the same altitude. At that point; the supervisor behind me said words which I took to mean that I should climb Aircraft Y. Immediate climb to FL230 was issued. When the microphone key was released; Aircraft Y advised that he thought he had stepped on me; that he was descending and had the traffic in sight. During the next minute; Aircraft X did climb to 3000; five miles lateral separation was established; Aircraft X got the visual approach clearance; and Aircraft Y was cleared on course and climbed. Recommendation; the descent of Aircraft X was totally unexpected. Training on potential fallout of clearances when certain aspects are implicit rather than explicit could be done. There are several ways that the situation as it developed could have been handled differently. The departure could have been held on the ground. The Tower Controller could have been given a heading to issue to the departure; in order to gain lateral separation more quickly. Restating the altitude to maintain (3000) could have been included in the 'enter right downwind' clearance. In place of the 'enter right downwind' clearance; a heading to fly could have been issued.