Public praise gay prince coming out (9)
I believe the answer is:
panegyric
'public praise' is the definition.
'panegyric' can be an answer for 'praise' (panegyric is a kind of praise). I'm not sure about the 'public' bit.
'gay prince coming out' is the wordplay.
'coming out' is an anagram indicator.
'gay'+'prince'='gayprince'
'gayprince' is an anagram of 'PANEGYRIC'.
Can you help me to learn more?
(Other definitions for panegyric that I've seen before include "Eulogy" , "words of tribute" , "Laudatory address" , "Speech of praise" , "encomium" .)