Biting right into the tart (5)
I believe the answer is:
acrid
'the tart' is the definition.
(I've seen this before)
'biting right into' is the wordplay.
'biting' becomes 'acid' (I've seen this before).
'right' becomes 'r' (common abbreviation).
'into' indicates putting letters inside.
'acid' placed around 'r' is 'ACRID'.
(Other definitions for acrid that I've seen before include "Direly pungent" , "Sharp - biting" , "Bitter in smell, like smoke" , "Pungent; caustic" , "Stinging" .)