Fife to get the better of Dundee at the end (4)
I believe the answer is:
pipe
'fife' is the definition.
(thesaurus)
'get the better of dundee at the end' is the wordplay.
'get the better of' becomes 'pip' (to pip someone is narrowly beat them).
'at the end' suggests the final letters.
The last letter of 'dundee' is 'e'.
'pip'+'e'='PIPE'
'to' is the link.
(Other definitions for pipe that I've seen before include "Possibly a churchwarden" , "Means of conveying" , "Tobacco is smoked in it" , "'Tube for water or gas, say (4)'" , "Water carrier" .)