Regularly ignored droopy tail of Rex? (5)
I believe the answer is:
royal
'of rex?' is the definition.
('rex' is Latin for king)
'regularly ignored droopy tail' is the wordplay.
'regularly ignored' indicates alternate letters (letters removed at regular intervals).
'droopy'+'tail'='droopytail'
The alternate letters of 'droopytail' are 'ROYAL'.
(Other definitions for royal that I've seen before include "Of sovereigns" , "William, say" , "Kingly or queenly" , "Splendid!" , "- - Shakespeare Company (RSC)" .)