Check on reportedly pricey animal (8)
I believe the answer is:
reindeer
'animal' is the definition.
(thesaurus)
'check on reportedly pricey' is the wordplay.
'check' becomes 'rein' (both can mean to control or limit).
'on' means one lot of letters go next to another.
'reportedly' indicates a 'sounds like' (homophone) clue.
'pricey' becomes 'dear' ('dear' can be a synonym of 'pricey').
'dear' sounds like 'deer'.
'rein'+'deer'='REINDEER'
(Other definitions for reindeer that I've seen before include "Dancer's one" , "Animal from 1 across" , "Antlered subarctic creature" , "Large animal of northern regions" , "Animal that pulls Santa's sleigh" .)