Crossword Genius

I'm not obliged, but try to leave the cost, generally (7)

Ross

I believe the answer is:

ingrate

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'cost generally' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for ingrate that I've seen before include "One unappreciative" , "Thankless sort" , "He doesn't appreciate" , "Unappreciative character" , "one offers no thanks" .)

I've seen this clue in The Independent.
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