Were upset about a point but start again (5)
I believe the answer is:
renew
'start again' is the definition.
(to renew something is to start it again)
'were upset about a point' is the wordplay.
'upset' indicates an anagram.
'about' is an insertion indicator.
'a point' becomes 'n' (N is an example).
'were' with letters rearranged gives 'reew'.
'reew' placed around 'n' is 'RENEW'.
'but' is the link.
(Other definitions for renew that I've seen before include "Regenerate" , "Start afresh" , "Transform born-again" , "Give fresh strength to" , "Give fresh life to" .)