Former librarian advising trade exhibition, just starting (4)
I believe the answer is:
late
'former' is the definition.
(thesaurus)
'librarian advising trade exhibition just starting' is the wordplay.
'just starting' suggests taking the first letters.
The first letters of 'librarian advising trade exhibition' is 'LATE'.
(Other definitions for late that I've seen before include "After the usual time" , "Not yet arrived - departed" , "Delayed; dead" , "Behind schedule" , "near the end" .)