To dedicate to pirate is cutting in itself (8)
I believe the answer is:
inscribe
'to dedicate' is the definition.
(inscribing is a kind of dedicating)
'pirate is cutting in itself' is the wordplay.
'pirate' becomes 'crib' (I've seen this before).
'is cutting' indicates putting letters inside (some letters cut their way into a word).
'itself' becomes 'se'.
'in'+'se'='inse'
'crib' going within 'inse' is 'INSCRIBE'.
'to' is the link.
(Other definitions for inscribe that I've seen before include "Engrave or write upon" , "Put dedication into" , "Write upon, formally perhaps" , "Engrave; enter (name in list)" , "Write or cut words into a surface" .)