The setter's visibly embarrassed to admit papa, behold, was begging (8)
I believe the answer is:
implored
'was begging' is the definition.
I can't tell whether this defines the answer.
'the setter's visibly embarrassed to admit papa behold' is the wordplay.
'the setter's' becomes 'im' (referring to the person who set the crossword).
'visibly embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'to admit' is an insertion indicator.
'papa' becomes 'P' (NATO / phonetic alphabet).
'behold' becomes 'lo' (archaic exclamation meaning 'look!').
'im'+'red'='imred'
'p'+'lo'='plo'
'imred' going around 'plo' is 'IMPLORED'.
Can you help me to learn more?
(Other definitions for implored that I've seen before include "Begged earnestly" , "Entreated, begged" .)