The green arrow is the speed trend vector showing predicted airspeed in 10 seconds:
2 Speed Trend Vector
Indicates predicted airspeed in ten seconds based on current acceleration or deceleration.
(Boeing 777 FCOMv2 10.10.4 - Flight Instruments, Displays - Controls and Indicators)
Other Boeing aircraft with a speed tape on the PFD (or ADI for early 757/767) have the same feature (I checked 737NG, 747-400, 747-8, 767 and 777 FCOMs). All have very similar descriptions, although the one for the 747-8 is more detailed:
The tip of the arrow indicates predicted airspeed in ten seconds based on airspeed,
inertial data, and winds. Rapidly changing wind speed or direction can affect
predicted airspeed with no change to indicated airspeed.
Airbus aircraft also have a very similar feature, as already explained in this question: What scale is the speed trend line on a PFD's ASI?