Over time, leave behind blooming good series! (7)
I believe the answer is:
outgrow
'over time leave behind' is the definition.
(leave something behind over time)
'blooming good series' is the wordplay.
'blooming' becomes 'out' (plants which have bloomed are 'out').
'good' becomes 'g' (abbreviation).
'series' becomes 'row' (I've seen this before).
'out'+'g'+'row'='OUTGROW'
(Other definitions for outgrow that I've seen before include "Become too big for" , "Get bigger" , "Leave (something) behind as one matures" , "Develop beyond" , "Get too big for" .)