Profundity of department head's introduction (5)
I believe the answer is:
depth
'profundity' is the definition.
(I know that profundity can be written as depth)
'department head's introduction' is the wordplay.
'department' becomes 'dept'.
'introduction' says to take the initial letters.
The first letter of 'heads' is 'h'.
'dept'+'h'='DEPTH'
'of' acts as a link.
(Other definitions for depth that I've seen before include "Intensity; profundity" , "sometimes leading to charge for sailors at war?" , "Distance from top down as in water" , "Distance downwards" , "Military life; vulgarly artificial" .)