Dean half-cut on organ offers transfer (7)
I believe the answer is:
deliver
'transfer' is the definition.
(I know that deliver is a more specific form of the action bring)
'dean half-cut on organ' is the wordplay.
'half cut' indicates taking half.
'on' says to put letters next to each other.
'organ' becomes 'liver' (liver is a kind of organ).
'dean' halved is 'de'.
'de'+'liver'='DELIVER'
'offers' is the link.
(Other definitions for deliver that I've seen before include "Highwaymen's cry - stand and ......." , "Transfer and hand over" , "Convey, transport (goods)" , "Bring to a destination and hand over" , "Hand over - release" .)