A knock that appears when the car pulls away and vanishes once moving needs a change in load direction. As you release the clutch or apply torque, the drivetrain and the exhaust rock against their mounts. Something in that chain has clearance, and it is being taken up and given back as a clunk.
The key split is exhaust versus driveline. An exhaust knock is a single dull thud from behind the driver, once per pull-away. A driveline knock is sharper, can repeat, and may come with a shunt. If the noise is a soft thud rather than a hard clack, start with the mounting.
Rubber hangers exist to allow movement, which is exactly why they can knock. Under torque reversal the system swings on its mounts, and a worn, soft or wrongly stiff hanger lets that swing become large enough to strike something. The knock is that strike, and it happens in one direction only.
Have someone watch while you load it. With the handbrake on and the car in gear, let the clutch bite gently and watch the rear section. Healthy hangers let it move a little and stay clear; worn ones let it swing into contact. Keep it brief, and keep nobody underneath.
Slip joints allow thermal expansion, which means they are free to move under torque too. A joint clamped but not fully seated can slide a little when the system rocks, producing a knock at the joint rather than at the body. The sound is more click than thud and comes from one identifiable place.
Mark the joint with a paint pen, drive normally for a while, then look at the mark. If the two halves have moved relative to each other, the joint is sliding and the clamp is not doing its job. That is a mounting geometry problem as much as a clamp problem, because a joint being pulled apart will always slide.
A worn engine mount knocks on pull-away in a way that sounds exactly like an exhaust knock, and it is the most commonly missed cause. A soft mount lets the engine rock further, which both loads the exhaust and makes its own noise. The difference is that you feel it as well as hear it.
Load the engine gently while watching the bay. If the engine lifts noticeably on one side, the mount is tired; a healthy one allows a small amount of movement and then stops. Do this before replacing exhaust parts, because a new titanium exhaust system hung on worn mounts will knock exactly as the old one did.
Even a well-mounted system knocks if the alignment lets a clearance close as it moves. A pipe close to a subframe at rest will touch the moment the system swings. This is more common on lowered cars and on systems assembled on a lift with the suspension hanging, where the geometry is not the geometry at ride height.
Check clearance at ride height, on ramps or a drive-on lift, then again with a jack under the suspension. A gap that looks generous at droop can close completely at ride height, which is exactly when the knock appears. Where the car is a known model, the shop by vehicle listings show which system was designed for the chassis.
With the engine off, grab the rear section and rock it firmly by hand in every direction. A healthy system moves against its hangers and stops. A knock you can reproduce by hand is one you can find by eye, because the contact becomes obvious once you know which direction produces it.
If the knock only happens under real driving load and never by hand, the movement involved is larger than a hand can make, which points at a mount rather than a clearance. If it happens by hand too, it is clearance or a worn hanger. That test tells you whether to look at rubber or steel.
