Late finish is obstacle (4,3)

I believe the answer is:

dead end

'is obstacle' is the definition.
(thesaurus)

'late finish' is the wordplay.
'late' becomes 'dead' (similar in meaning).
'finish' becomes 'end' (synonyms).
'dead'+'end'='DEAD-END'

(Other definitions for dead end that I've seen before include "Blind alley or situation without prospects" , "that's leading nowhere" , "Where no progress can be made" , "A blind alley, point of no further progress" , "Situation with no way forward" .)

I've seen this clue in The Sun.

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