Start to thump eccentric (7)
I believe the answer is:
offbeat
'eccentric' is the definition.
(offbeat means eccentric or unexpected)
'start to thump' is the wordplay.
'start' becomes 'off' (as in 'from the off').
'to thump' becomes 'beat' (synonyms).
'off'+'beat'='OFFBEAT'
(Other definitions for offbeat that I've seen before include "Wacky; syncopated" , "Strikingly unconventional" , "Way-out" , "Kooky" , "Unusual or unconventional - perhaps in music" .)