Picked up actress associated with Burton, maker of garments (6)
I believe the answer is:
tailor
'maker of garments' is the definition.
(I've seen this before)
'picked up actress associated with burton' is the wordplay.
'picked up' shows a homophone (sound like).
'actress associated with burton' becomes 'taylor' (Elizabeth Taylor, wife of Richard Burton).
'taylor' is a homophone of 'TAILOR'.
(Other definitions for tailor that I've seen before include "fitter" , "person before soldier and sailor in list" , "Maker of clothes for men" , "Maker of men's suits" , "Maker of fitted clothes" .)