Pester people in the run-up (7)
I believe the answer is:
torment
'pester' is the definition.
(I've seen this before)
'people in the run-up' is the wordplay.
'people' becomes 'men' (men are people).
'in' means one lot of letters goes inside another.
'the run' becomes 'trot' (trot is a kind of run).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'trot' back-to-front is 'tort'.
'men' inserted into 'tort' is 'TORMENT'.
(Other definitions for torment that I've seen before include "Tease unkindly" , "Punish" , "Anguish" , "Harry" , "More TNT (anag.)" .)