Some time ago no athlete would have sworn (2,4)
I believe the answer is:
'sworn' is the definition.
(having sworn an oath)
'some time ago no athlete' is the wordplay.
'some' indicates a hidden word (some of the parts of the word are used).
'ON OATH' can be found hidden inside 'time ago no athlete'.
'would have' is the link.
(Other definitions for on oath that I've seen before include "Sworn to speak the truth" , "Bound to speak the truth" .)