The goat's showing some personal image (3)
I believe the answer is:
ego
'personal image' is the definition.
'ego' can be an answer for 'image' (I have seen 'Image of oneself ' mean 'ego' so perhaps 'image' could also mean 'ego'). I'm not certain of the 'personal' bit.
'the goat's showing some' is the wordplay.
'some' indicates a hidden word.
'EGO' can be found hidden inside 'the goats showing'.
Can you help me to learn more?
(Other definitions for ego that I've seen before include "Person's sense of self" , "Vowel to disappear, < say another" , "Morale" , "One's self image" , "Conscious mind" .)