Old ship builder bites tip of tongue, having sworn (2,4)
I believe the answer is:
on oath
'sworn' is the definition.
(having sworn an oath)
'old ship builder bites tip of tongue' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'ship builder' becomes 'Noah' (Noah's ark).
'bites' indicates putting letters inside.
'tip of' suggests taking the first letters.
The first letter of 'tongue' is 't'.
'noah' going around 't' is 'noath'.
'o'+'noath'='ON OATH'
'having' is the link.
(Other definitions for on oath that I've seen before include "Bound to speak the truth" , "Sworn to speak the truth" .)