Parrot kept in container that's most tacky (8)
I believe the answer is:
cheapest
'most tacky' is the definition.
('cheap' can be a synonym of 'tacky')
'parrot kept in container' is the wordplay.
'parrot' becomes 'ape' (I've seen this before).
'kept in' indicates putting letters inside.
'container' becomes 'chest' (chest is a kind of container**).
'ape' going within 'chest' is 'CHEAPEST'.
'that's' is the link.
(Other definitions for cheapest that I've seen before include "The space (anag.)" , "Most vile" , "Most inferior" , "Most economical" , "Set peach in least expensive category" .)