Distance down to Department H (5)
I believe the answer is:
depth
'distance down' is the definition.
(I've seen this in another clue)
'department h' is the wordplay.
'department' becomes 'dept'.
'dept'+'h'='DEPTH'
'to' is the link.
(Other definitions for depth that I've seen before include "Intensity (of emotion)" , "Distance from the surface to the bottom" , "Profoundness" , "Intensity; profundity" , "Thoroughness" .)