Rex inclined to be ecstatic (4)
I believe the answer is:
rapt
'ecstatic' is the definition.
(thesaurus)
'rex inclined' is the wordplay.
'rex' becomes 'r' (common abbreviation e.g. GR=George Rex, King Georg).
'inclined' becomes 'apt' ('apt' can be similar in meaning to 'inclined').
'r'+'apt'='RAPT'
'to be' is the link.
(Other definitions for rapt that I've seen before include "Part of being intent and absorbed" , "Delighted" , "Gripped" , "Taken up entirely" , "Absorbed, fascinated" .)