Had the experience of a heartening, fantastic educated guess (6)
I believe the answer is:
tasted
'had' is the definition.
(tasting is a kind of having)
'experience of a heartening fantastic educated guess' is the wordplay.
I cannot really understand how this works, but
'experience' could be 'taste' (taste can mean to experience or try out) and 'taste' is present in the answer.
A single letter 'd' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
'the' acts as a link.
Can you help me to learn more?
(Other definitions for tasted that I've seen before include "Sampled (food)" , "Tried for flavour" , "Sampled (a food/drink)" , "Sampled the flavour" , "Samples" .)