Quick extra-terrestrial gets meat cut (7)
I believe the answer is:
brisket
'meat cut' is the definition.
(I've seen this in another clue)
'quick extra-terrestrial' is the wordplay.
'quick' becomes 'brisk' (I've seen this before).
'extra terrestrial' becomes 'et' (abbreviation - like in the famous 1982 movie).
'brisk'+'et'='BRISKET'
'gets' acts as a link.
(Other definitions for brisket that I've seen before include "Meat from a cow's chest" , "Cut of beef from near the ribs" , "Breast of four-legged animal" , "Meat cut from the breast of an animal" , "Bet kris the cut of beef" .)