Fire-breathing monster created by artist under agreement (7)
I believe the answer is:
chimera
'fire-breathing monster' is the definition.
(I've seen this before)
'artist under agreement' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'under' means one lot of letters go next to another.
'agreement' becomes 'chime' (I am not sure about this - if you are sure you should believe this answer much more).
'ra' after 'chime' is 'CHIMERA'.
'created by' is the link.
Can you help me to learn more?
(Other definitions for chimera that I've seen before include "Lion-headed monster" , "Fantastic creation of the mind, like Greek mythical monster" , "Wild or impossible idea" , "eaders of radio appear after jingle" , "Mythical monster, part lion, goat and serpent" .)