Grind last bit of pepper -- a pinch! (3,4)
I believe the answer is:
rat race
'grind' is the definition.
(I've seen this in another clue)
'last bit of pepper a pinch' is the wordplay.
'last bit of' says to take the final letters.
'pinch' becomes 'trace' (I've seen this before).
The last letter of 'pepper' is 'r'.
'r'+'a'+'trace'='RAT-RACE'
(Other definitions for rat race that I've seen before include "Competitive way of life" , "keen contest" , "Hectic futile activity" , "Competitive struggle for wealth or power" , "keen competition" .)