Primitive man demanding immediate attention (6)
I believe the answer is:
Here is my best explanation:
'demanding immediate attention' is the definition.
'primitive man' is the subsidiary indication.
'primitive' becomes 'ur'.
'man' becomes 'gent' (gent is a kind of man**).
(Other definitions for urgent that I've seen before include "Needing immediate action", "Pressing, imperative", "Requiring immediate action", "Of immediate importance", "Demanding immediate attention", "Pressing, immediate", "Pressing, burning", "Needing immediate attention, don't delay", "Calling for immediate attention" and "Important and in a hurry".)