Blooming drag to go west from the centre (7)
I believe the answer is:
outward
'from the centre' is the definition.
(moving from the centre)
'blooming drag to go west' is the wordplay.
'blooming' becomes 'out' (plants which have bloomed are 'out').
'drag' becomes 'draw' (synonyms).
'to go west' is a reversal indicator (to go west can euphemistically mean to die).
'draw' back-to-front is 'ward'.
'out'+'ward'='OUTWARD'
(Other definitions for outward that I've seen before include "(In the direction of the) exterior" , "Ostensible" , "Towards the exterior" , "Apparent" , "Away from port" .)