Difficult time — extremely upset (7)
I believe the answer is:
testing
'difficult' is the definition.
(I've seen this before)
'time extremely upset' is the wordplay.
'extremely' suggests removing the centre.
'upset' becomes 'sting' (I can't justify this - if you can you should believe this answer much more).
'time' with its centre taken out is 'te'.
'te'+'sting'='TESTING'
Can you help me to learn more?
(Other definitions for testing that I've seen before include "of a difficult nature" , "Examining" , "... conducting exam" , "Trying out" , "Subjecting to 15 ac" .)