Reading's boss on the way out, their director shared (8)
I believe the answer is:
studying
'reading's' is the definition.
('study' can be a synonym of 'read')
'boss on the way out their director shared' is the wordplay.
I cannot quite understand how this works, but
'boss' could be 'stud' (both can mean a metal decoration) and 'stud' is found within the answer.
'way' could be 'n' (Compass direction - North) and 'n' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for studying that I've seen before include "In education" , "Reading carefully with the intention to remember" , "Doing what a student should" , "Acquiring knowledge" .)
