Director finally cutting our bit out -- it's a wrap! (7)
I believe the answer is:
burrito
'a wrap' is the definition.
(I know that burrito is a type of sandwich wrap)
'director finally cutting our bit out' is the wordplay.
'finally' says to take the final letters.
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
The last letter of 'director' is 'r'.
'our'+'bit'='ourbit'
'ourbit' anagrammed gives 'burito'.
'r' placed into 'burito' is 'BURRITO'.
'it's' acts as a link.
(Other definitions for burrito that I've seen before include "Tortilla folded around a savoury filling" , "that's eaten in Mexico" , "Mexican dish - rub trio (anag)" , "Mexican food" , "Mexican dish of tortilla folded around a filling" .)