Not serious under pressure in difficult situation (6)
I believe the answer is:
plight
'difficult situation' is the definition.
(I've seen this before)
'not serious under pressure' is the wordplay.
'not serious' becomes 'light' ('light' is the opposite to 'serious').
'under' means one lot of letters go next to another (below, in a down clue).
'pressure' becomes 'p' (scientific abbreviation).
'light' after 'p' is 'PLIGHT'.
'in' acts as a link.
(Other definitions for plight that I've seen before include "Serious predicament" , "Unlucky situation; promise" , "State" , "Quandary, predicament" , "Dangerous or difficult situation" .)