Burrowing insect having one grumble, to penetrate a set of books (9,3)

I believe the answer is:

carpenter ant

'burrowing insect' is the definition.
(type of ant which burrows)

'grumble to penetrate a set of books' is the wordplay.
'grumble' becomes 'carp' (I've seen this in another clue).
'to penetrate' becomes 'enter' (I've seen this before).
'set of books' becomes 'NT' (New Testament).
'carp'+'enter'+'a'+'nt'='CARPENTER-ANT'

'having one' is the link.

I've seen this clue in The Times.

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