Small piece of meat with one of the chips (6)
I believe the answer is:
Here is my best explanation:
'small piece' is the definition.
(I've seen this before)
'meat with one of the chips' is the subsidiary indication.
'meat' becomes 'liver' (liver is a kind of meat).
'with' says to put letters next to each other.
'one of the chips' becomes 's' (I can't explain this - if you can you should give a lot more credence to this answer).
'liver' put after 's' is 'sliver'.
'of' is the link.
(Other definitions for sliver that I've seen before include "Thin splinter", "Thin fragment or slice", "Small thin sharp piece", "Narrow sharp fragment", "Tiny slice, splinter", "Thin strip cut from glass or wood", "Thin sharp bit, of wood say", "Small, thin slice", "Shard" and "Bit".)