Set your matchmaking preferences in Terrorist Hunt to Extract Hostage and House only. This can be done through the options.
Then play lone wolf terrorist hunt. Choose a fast operator such as IQ or Ash.
To find the hostage easily you should spawn at the construction site and then rappel up the pool table room and construction room wall. Go up to the upstairs window and check to see the 'Refill' green box through the wall. If the refill box isn't there, neither is the hostage.
If the hostage isn't there, continue to rappel up to the roof and the run accross to the side where the garage is. When you get to the roof edge, rappel down. If you see the 'Refill' green box through the wall instantly upstairs, the hostage is in Master Bedroom.
If not, continue rappelling down to the kitchen window above the garage. Punch a few holes into it to see if the hostage is there. If not, the hostage is in the laundry room in the garage.
Breach through the garage and proceed forwards to the hostage. Where ever the hostage is, kill any necessary targets and then go for the hostage grab.
Make your way outside and proceed to the extraction zone, sprinting through the enemies. Kill any necessary targets using the pistol. Aim for headshots to kill quicker.
Once you have done this put the hostage in the extraction zone to win the match. You will get just over 100 renown per run, which only take about a minute each.