Important man by Ulster's borders (6)
I believe the answer is:
urgent
'important' is the definition.
(I've seen this before)
'man by ulster's borders' is the wordplay.
'man' becomes 'gent' (gent is a kind of man).
'by' means one lot of letters go next to another.
'borders' means to remove the middle letters (only the edge or border letters remain).
'ulster' with its centre taken out is 'ur'.
'gent' after 'ur' is 'URGENT'.
(Other definitions for urgent that I've seen before include "Pressing, burning" , "Pressing, imperative" , "Demanding immediate attention" , "Requiring speedy action" , "Needing early action" .)