Fragment of anarchic chants (6)

I believe the answer is:

snatch

'fragment' is the definition.
(as in hearing a snatch of a song)

'anarchic chants' is the wordplay.
'anarchic' is an anagram indicator.
'chants' with letters rearranged gives 'SNATCH'.

'of' is the link.

(Other definitions for snatch that I've seen before include "A bar or two" , "pull" , "American kidnapping" , "Seize quickly and eagerly" , "bag" .)

I've seen this clue in The Irish Times and the Irish Times (Crosaire).

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