Half finish a grid (cryptic) - that's unbecoming (5,3)
I believe the answer is:
infra dig
'unbecoming' is the definition.
(thesaurus)
'half finish a grid cryptic' is the wordplay.
'half' suggests halving the letters.
'cryptic' indicates an anagram.
'finish' cut in half is 'fin'.
'fin'+'a'+'grid'='finagrid'
'finagrid' is an anagram of 'INFRA DIG'.
'that's' acts as a link.
(Other definitions for infra dig that I've seen before include "Beneath oneself (from Latin)" , "Such as one would not stoop to" , "degrading" , "Demeaning (Latin)" , "Unworthy" .)