Attest to a very absorbing Kipling poem (6)
I believe the answer is:
verify
'attest' is the definition.
(I know that attest is a more specific form of the action the verify)
'very absorbing kipling poem' is the wordplay.
'absorbing' is an insertion indicator.
'kipling poem' becomes 'If' (poem by Rudyard Kipling).
'very' enclosing 'if' is 'VERIFY'.
'to a' is the link.
(Other definitions for verify that I've seen before include "Confirm the truth of" , "Ascertain truth or accuracy" , "Check the truth of" , "Support" , "Check (facts)" .)