Not on — Telegraph, evidently worried, showed sign of panic (15)

I believe the answer is:

hyperventilated

'showed sign of panic' is the definition.
(someone panicking might hyperventilate)

'not on telegraph evidently worried' is the wordplay.
'not' indicates named letters should be taken away.
'on' becomes 'leg' (cricket term, fielding positions).
'worried' is an anagram indicator.
'telegraph'+'evidently'='telegraphevidently'
'telegraphevidently' with 'leg' taken out is 'teraphevidently'.
'teraphevidently' is an anagram of 'HYPERVENTILATED'.

I've seen this clue in The Guardian.

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