Urgency shown by media certain to lose face (8)
I believe the answer is:
pressure
'urgency' is the definition.
(pressure is a kind of urgency)
'by media certain to lose face' is the wordplay.
'by' says to put letters next to each other.
'media' becomes 'press' (the press is part of the media).
'certain' becomes 'sure' (synonyms).
'to lose face' means to remove the first letter (I've seen 'losing face' mean this).
'sure' with its initial letter taken off is 'ure'.
'press' next to 'ure' is 'PRESSURE'.
'shown' is the link.
(Other definitions for pressure that I've seen before include "Force per unit area" , "Force measured in pascals" , "A force that compels" , "Force, stress, strain" , "Type of organised group which tries to influence politicians" .)