Wax lyrical in this way entering quarters (7)
I believe the answer is:
enthuse
'wax lyrical' is the definition.
(both can mean to speak enthusiastically)
'in this way entering quarters' is the wordplay.
'in this way' becomes 'thus' (synonyms).
'entering' indicates putting letters inside.
'quarters' becomes 'ene' (I am not sure about this - if you are sure you should believe this answer much more).
'thus' placed within 'ene' is 'ENTHUSE'.
(Other definitions for enthuse that I've seen before include "Show intense approval" , "Show eager interest and liking" , "Inspire with keenness" , "Appear keenly interested" , "Express eager enjoyment, interest or approval" .)