Animal looks right in stockings! (5)
I believe the answer is:
horse
'animal' is the definition.
(type of animal)
'right in stockings' is the wordplay.
'right' becomes 'r' (abbreviation).
'in' means one lot of letters goes inside another.
'stockings' becomes 'hose' (hose refers to stockings, tights etc).
'r' inserted inside 'hose' is 'HORSE'.
'looks' is the link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for horse that I've seen before include "Animal with withers" , "Equipment in gym" , "This common sense is of equine origin" , "eg Shire" , "Animal featuring in the sport of kings" .)