Devoted about tigers - terribly reputable (11)
I believe the answer is:
prestigious
'reputable' is the definition.
(similar in meaning)
'devoted about tigers terribly' is the wordplay.
'devoted' becomes 'pious' (I can't justify this - if you can you should believe this answer much more).
'about' means one lot of letters goes inside another.
'terribly' indicates anagramming the letters.
'tigers' with letters rearranged gives 'restig'.
'pious' enclosing 'restig' is 'PRESTIGIOUS'.
Can you help me to learn more?
(Other definitions for prestigious that I've seen before include "Influential" , "Having high status" , "Having glamour and influence" .)