Save channel broadcast that's smooth (5-6)

I believe the answer is:

clean-shaven

'smooth' is the definition.
(thesaurus)

'save channel broadcast' is the wordplay.
'broadcast' is an anagram indicator.
'save'+'channel'='savechannel'
'savechannel' anagrammed gives 'CLEAN-SHAVEN'.

'that's' is the link.

(Another definition for clean-shaven that I've seen is " Unbearded".)

I've seen this clue in The Mirror.

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