There is no article at all in the MT text before ברית in Daniel 9:27. So you can translate it as any of
- The Covenant
- A covenant
To decide the best translation you need to consider the context.
Since this verse appears to describe a sequence in which the annointed king at first upholds the Covenant, then disolves the sacrificial cult, establishes foreign worship and finally brings physical destruction, it would appear that the covenant referred to in this verse is specifically the torah of Moses. So either 1) "Covenant" or 2) "the Covenant" fits the context better than 3) "a covenant". The first option is closer to the Hebrew expression. The second is clearer to the English speaking reader with no knowledge of Hebrew.