One's embarrassed for ages (4)
I believe the answer is:
eons
'ages' is the definition.
(eon is a kind of age)
'one's embarrassed' is the wordplay.
'one's' anagrams to 'EONS'.
But, I am not clear how this is indicated.
'for' acts as a link.
Can you help me to learn more?
(Other definitions for eons that I've seen before include "Times" , "Long periods of time - noes have it" , "Years and years" , "Divisions of archaeological time" , "Very long periods (US)" .)