Hospital department starts to get some dimension (5)
I believe the answer is:
depth
'some dimension' is the definition.
(I've seen this in another clue)
'hospital department starts' is the wordplay.
'hospital' becomes 'H' (abbreviation for hospital).
'department' becomes 'dept'.
'starts' says to put letters next to each other.
'h' after 'dept' is 'DEPTH'.
'to get' acts as a link.
(Other definitions for depth that I've seen before include "Intensity (of emotion)" , "Distance from top down as in water" , "Insight" , "Distance downwards" , "Profoundness" .)