Pressing case for unpopular fellow (6)
I believe the answer is:
urgent
'pressing' is the definition.
('urgent' can be a synonym of 'pressing')
'case for unpopular fellow' is the wordplay.
'case for' suggests removing the centre (the letters which encase the others are used).
'fellow' becomes 'gent' (I've seen this before).
'unpopular' with its centre removed is 'ur'.
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "High priority" , "Of immediate importance" , "Extremely pressing" , "Pressing, imperative" , "Requiring early action" .)