One accidentally gobbles up terribly old piece of pasta (6)
I believe the answer is:
noodle
'piece of pasta' is the definition.
'noodle' can be an answer for 'pasta' (noodle is a kind of pasta). I am not certain of the 'piece of' bit.
'one accidentally gobbles up terribly old' is the wordplay.
'accidentally' indicates anagramming the letters (a chaotic or accidental ordering of the letters).
'gobbles' means one lot of letters goes inside another.
'up' says the letters should be written backwards (in down clue: letters go upwards).
'terribly' becomes 'ld' (I can't explain this - if you can you should give a lot more credence to this answer).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'ld'+'o'='ldo'
'ldo' backwards is 'odl'.
'one' anagrammed gives 'noe'.
'noe' enclosing 'odl' is 'NOODLE'.
Can you help me to learn more?
(Other definitions for noodle that I've seen before include "String of pasta" , "strip in the kitchen" , "Nitwit" , "Slangy head or pasta strip" , "See silly person" .)