If 240Hz monitor is tearing, the cure is almost always syncing the GPU to the panel - VRR, V-Sync or a frame cap - rather than buying new hardware.
Quick Answer
To stop screen tearing on 240Hz monitor, enable adaptive sync (G-Sync or FreeSync) in the GPU driver, turn on the monitor's VRR setting, and cap frames a few fps below the panel's refresh - for example 141 fps on a 144Hz display. These steps remove tearing without adding noticeable input lag.
Per-game settings that keep 240Hz monitor tear-free
Use each game's built-in frame limiter or borderless-fullscreen mode where exclusive fullscreen misbehaves with VRR. On 240Hz monitor, match the in-game cap to your driver cap so the two do not fight and re-introduce a tearing line.
Frame caps and V-Sync that suit 240Hz monitor
Cap frames a few fps under the refresh ceiling - 141 on 144Hz, 237 on 240Hz - so the GPU stays inside the VRR window. Pair the cap with low-latency V-Sync only if a thin tearing line persists at the very top of the screen.
Enable adaptive sync for 240Hz monitor
Open the GPU control panel and switch on G-Sync or FreeSync, then enable the matching VRR setting in the monitor's on-screen menu. With a 240Hz panel running variable refresh, VRR matches refresh to your actual frame rate so the tearing line disappears across the supported range.
FAQ
Why does tearing return after a driver update on 240Hz monitor?
Updates sometimes reset VRR or refresh settings to default. After updating, re-check that adaptive sync is on in the driver and the monitor menu, and that 240Hz monitor is still running at full refresh in Windows.
Is G-Sync or FreeSync better for 240Hz monitor?
Both remove tearing well; choose the one your GPU and panel support. Most modern monitors handle adaptive sync from either brand, so on 240Hz monitor the practical choice is whichever your hardware lists.
Does fullscreen mode matter for tearing on 240Hz monitor?
It can. Some titles handle VRR better in exclusive fullscreen, others in borderless. If 240Hz monitor still tears, switch the game's display mode and confirm only one frame cap is active.
Pro Tip
Check the cable and full refresh in Windows, then enable VRR to keep 240Hz monitor tear-free.