Big cat in cooking vessel on the right (7)
I believe the answer is:
panther
'big cat' is the definition.
(panthers are big cats)
'cooking vessel on the right' is the wordplay.
'cooking vessel' becomes 'pan' (I've seen this in another clue).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'right' becomes 'r' (common abbreviation).
'pan'+'the'+'r'='PANTHER'
'in' is the link.
(Other definitions for panther that I've seen before include "Black leopard" , "Big cat" , "big pussycat" , "animal!" , "Bagheera?" .)