Eastern Times colour covers cold and obsolete (7)
I believe the answer is:
extinct
'obsolete' is the definition.
(thesaurus)
'eastern times colour covers cold' is the wordplay.
'eastern' becomes 'e'.
'times' becomes 'x' (multiplication sign).
'colour' becomes 'tint' (tint is a kind of colour**).
'covers' indicates putting letters inside.
'cold' becomes 'c' (eg on taps).
'tint' enclosing 'c' is 'tinct'.
'e'+'x'+'tinct'='EXTINCT'
'and' is the link.
(Other definitions for extinct that I've seen before include "No longer extant" , "No longer erupting" , "Dead - obsolete - extinguished" , "never to be seen again" , "Permanently inactive" .)