Centre succeeded in time of growth (5)
I believe the answer is:
bosom
'centre' is the definition.
(bosom can figuratively mean a centre or core)
'succeeded in time of growth' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'in' indicates putting letters inside.
'time of growth' becomes 'boom' (period of financial growth).
's' inserted inside 'boom' is 'BOSOM'.
(Other definitions for bosom that I've seen before include "Chest; very close (friend)" , "A close affectionate and protective acceptance" , "(Female's) chest" , "Woman's breast" , "Female breasts" .)