Times Cryptic Hotline gives 'rock fragment' (8)

I believe the answer is:

xenolith

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'rock fragment' is the definition.
The definition suggests a singular noun which matches the answer.

'times cryptic hotline' is the wordplay.
'times' becomes 'x' (2 times 4 is 2 x 4).
'cryptic' indicates an anagram (a cryptic or obscure order of the letters).
'hotline' with letters rearranged gives 'enolith'.
'x'+'enolith'='XENOLITH'

'gives' acts as a link.

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