To set about messenger, being cross (7)
I believe the answer is:
tangelo
'being cross' is the definition.
(cross-bred fruit)
'to set about messenger' is the wordplay.
'set about' indicates putting letters inside.
'messenger' becomes 'angel' (heavenly messenger).
'to' going around 'angel' is 'TANGELO'.
(Other definitions for tangelo that I've seen before include "Mixed fruit" , "Citrus fruit hybrid" , "Citrus hybrid - goal net (anag)" , "fruitful merger?" , "one cross, sour" .)