Alpha-gamma connector (4)
I believe the answer is:
'alpha-gamma connector' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for beta that I've seen before include "less than perfect mark" , "Greek character - not quite top-notch" , "Greek letter -- second in order of importance" , "Second Greek letter, B" , "sort of test" .)