Star announced support for record company's move overseas (8)
I believe the answer is:
emigrate
'move overseas' is the definition.
(I've seen this before)
'star announced support for record company's' is the wordplay.
'star' becomes 'great' (one of the greats).
'announced' shows a homophone (sound like).
'support for' says to put letters next to each other (in a down clue, some letters \'support\' others).
'record company' becomes 'EMI' (British record label).
'great' sounds like 'grate'.
'grate' put after 'emi' is 'EMIGRATE'.
(Other definitions for emigrate that I've seen before include "Move overseas" , "don't come back!" , "Go to live and work in another country" , "Leave home" , "Tiger Mae has gone abroad to live, oddly" .)