Horse has a ban lifted (4)
I believe the answer is:
arab
'horse' is the definition.
(Arab is an example)
'a ban lifted' is the wordplay.
'ban' becomes 'bar' (I've seen this before).
'lifted' shows that the letters should be reversed in order (going up in down clue).
'bar' in reverse letter order is 'rab'.
'a'+'rab'='ARAB'
'has' is the link.
(Other definitions for arab that I've seen before include "Saudi, perhaps - breed of horse" , "One from the Middle East or North Africa" , "Native of North Africa" , "Small, lively breed of horse" , "Horse of a breed originating in the Middle East" .)