The well is currently at a depth of 1155m after making progress of 116m this week. Casing operations are being completed.
Cobra, in PPL 190 about 13km east of the SE Gobe oilfield and 7km east of the Bilip oil discovery, was halted in February after some subsidence was observed at the well site.
The well is directed at the Iagifu Sandstone - the principal reservoir in the Gobe and SE Gobe fields - in a seismically defined sub-thrust prospect.
Oil Search said Cobra-1 is the first well in PNG to target a sub-thrust play as the primary target.
Participants in the Cobra-1A are operators Oil Search (62.556%), Murray Petroleum (26.497%) and Cue Energy (10.947%).
Elsehwhere in PNG, OIL Search has made 276 m of progress for the week at its NW Paua-1 ST3 well and is drilling ahead in an 8.5-inch by nine and seven-eighth inch hole.
To allow for a larger casing size, the hole is being drilled and opened concurrently.
The sidetrack is at 2883m of its total planned depth of 3600m.
The well targets the Toro and Digimu sandstones in a more optimal location on the known hanging-wall structure than the Paua-1x well that was drilled in the mid 1990s, according to Oil Search.
Participants in NW Paua are Oil Search at 52.5% and ExxonMobil at 47.5%.
And in Egypt, drilling at the Shahd SE-1 well has reached its total depth of 3063m and the well was logged.
Oil Search has identified a total of 17m of oil pay in the Upper and Lower Bahariya Sandstones and preparations are underway to start a production test over these areas.