Cup of tea left to get very cold? (7)

I believe the answer is:

chalice

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'cup' is the definition.
(chalice is a kind of cup)

'tea left to get very cold?' is the wordplay.
'tea' becomes 'cha' (cha is a type of tea).
'left' becomes 'L' (common abbreviation).
'to get' means one lot of letters go next to another.
'very cold?' becomes 'ice' (I've seen this before. I am not sure about the 'very' bit.).
'cha'+'l'+'ice'='CHALICE'

'of' acts as a link.

Can you help me to learn more?

(Other definitions for chalice that I've seen before include "Necessity for communion" , "Wine cup used at Christian Eucharist" , "Communion cup" , "Cup used in church" , "Church wine cup" .)

I've seen this clue in The Sun.

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