Profoundness of the department head, initially (5)
I believe the answer is:
depth
'profoundness' is the definition.
(I know that profoundness can be written as depth)
'department head initially' is the wordplay.
'department' becomes 'dept'.
'initially' indicates taking the first letters.
The first letter of 'head' is 'h'.
'dept'+'h'='DEPTH'
'of the' acts as a link.
(Other definitions for depth that I've seen before include "Intensity; profundity" , "Downward extent" , "Intensity (of emotion)" , "Measurement from front to back" , "Distance downwards" .)