I'm not sure that there is a term for Belegabteilung. In US hospitals, in any case, it's seen from the physician's point of view, i.e. the physician has privileges at a hospital. A Belegarzt, then, would be a physician who has privileges


The following explanation might help: If a hospital is equipped for a procedure, a physician earns the right to perform that procedure through a process known as "privileging." Privileging means that a physician has qualified for a specific privilege based on his or her training and experience. The privileging process identifies physicians as provisional, active or courtesy. Though the criteria for each designation varies, in general a physician with active privileges is one who regularly admits patients to a hospital and who provides continuous care to patients once admitted. A physician with provisional privileges is in the process (usually for a one-year period) of demonstrating that his or her education, training, experience and competence qualify him or her for active status. Finally, a physician with courtesy privileges is one who, though his or her experience and training qualify him or her to hold active privileges, does not regularly admit patients to the hospital for primary medical or surgical care and, therefore, is not granted all the privileges awarded to a member of the active staff. A physician maintains his or her privileges through a regular review of his or her performance, continued training and demonstrated ability.
If a physician has been granted active hospital privileges in an area, it signifies that the hospital has reviewed his or her expertise and evaluated his or her skills and determined he or she should be allowed to perform necessary procedures.
www.myhealth2000.com/hospitals/stjude/physician/privileges....

none

Belegarzt im Sinne des Sozialgesetzbuches ist ein nicht am Krankenhaus angestellter Vertragsarzt, der berechtigt ist, seine Patienten (Belegpatienten) im Krankenhaus unter Inanspruchnahme der hierfür
bereitgestellten Dienste, Einrichtungen und Mittel stationär oder teilstationär zu behandeln, ohne hierfür vom
Krankenhaus eine Vergütung zu erhalten.

Please see the info supplied by the AOK Bundesverband( very useful little glossary, too!)
Belegarztwesen SHI-physician-system with in-patient authorization (SHI meaning Social Health Insurance)


see:www.aok.de/bundesverband/lexikon/v/v23.html
This glossary translates Vertragsarzt as * panel doctor*, while
*SHI-authorized physician* is the suggested translation of "Belegarzt" in www.kbv.de/Homepage/service/Lexindx/D_tuv.html

(Unseld Medical dictionary quotes for Belegarzt: practitioner with hospital affiliation,while Belegkrankenhaus simply is "open hospital":sounds a bit vague).

In view of the above definition and considering the fact that the German medical system greatly differs from the American/English system I would support Ulrike's suggestion, namely to translate Belegarzt as physician with ( hopsital-treatment)privileges for Belegarzt.
Hope to have been of assistance!