Medieval tournament, not old, is fair (4)
I believe the answer is:
just
'fair' is the definition.
(I know that fair can be written as just)
'medieval tournament not old' is the wordplay.
'medieval tournament' becomes 'joust'.
'not' suggests deleting specific letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'joust' with 'o' taken out is 'JUST'.
'is' acts as a link.
(Other definitions for just that I've seen before include "Fair - precisely" , "By the skin of your teeth - equitable" , "Hardly" , "Quite" , "Morally right" .)