The daily struggle of people pursuing a renegade (3,4)
I believe the answer is:
rat race
'the daily struggle' is the definition.
(I've seen this before)
'people pursuing a renegade' is the wordplay.
'people' becomes 'race'.
'pursuing' means one lot of letters go next to another.
'a renegade' becomes 'rat' (I've seen this before).
'race' put after 'rat' is 'RAT RACE'.
'of' acts as a link.
(Other definitions for rat race that I've seen before include "unhealthy competition" , "life's futile struggle" , "Daily struggle to get on" , "Competitive routine with no time to relax" , "Competitive way of life" .)