Give away pouch with grain, if hiding (9)

I believe the answer is:

sacrifice

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'give away' is the definition.
(thesaurus)

'pouch with grain if hiding' is the wordplay.
'pouch with' becomes 'sac' (synonyms. I am not sure about the 'with' bit.).
'grain' becomes 'rice' (rice is a kind of grain).
'hiding' is an insertion indicator.
'rice' going around 'if' is 'rifice'.
'sac'+'rifice'='SACRIFICE'

Can you help me to learn more?

(Other definitions for sacrifice that I've seen before include "Immolate" , "Offering to a god" , "Renounce" , "Give up" , "Killed offering to a deity" .)

I've seen this clue in The Guardian.

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