Not sure whether you are arriving on UA or AC. AC has recently moved its flights from T3 to the G wing of the International Terminal. You exit the plane into the departures section and take the airside walkway without having to go through any further security (do NOT follow the signs to baggage claim as then you will have to re-enter the airside). Although the AC gates are close in, some UA gates in T3 are far away, so it could take 10 minutes to walk at a reasonable speed from one to the other. Likewise, if T3 is full, some UA flights can arrive or depart from the G wing, which UA uses as an overflow. So, if you are on-time, there should be no problem. If not, then you will be rushing or looking at being protected on a later flight.
Typically:
767 = 2-3-2 in coach (14% middles)
777 = 2-5-2 in coach (33% middles)
737 = 3-3 in coach (33% middles)
If you are flying to HNL on HA, note that HA flights are rarely late, so a late inbound would likely mean a missed connection.
HA doesn't fly from T3 so the OP can't be on HA.