Get a bit worried on going round (6)
I believe the answer is:
obtain
'get' is the definition.
('obtain' can be a synonym of 'get')
'a bit worried on going round' is the wordplay.
'worried' indicates anagramming the letters.
'going round' indicates putting letters inside.
'a'+'bit'='abit'
'abit' with letters rearranged gives 'btai'.
'btai' going inside 'on' is 'OBTAIN'.
(Other definitions for obtain that I've seen before include "Get, procure" , "Acquire or procure" , "Take possession of" , "Gain possession of" , "Get or lay hold of" .)