Paired but not connected means Windows remembers the device and its keys, but the connection itself is not coming up. The device may be off, out of range, still connected to a phone, or stuck on a stale link, and each of those has a different quick fix.
Fix it, in order
Connect it manually. Press Win + A to open Quick Settings and click the Bluetooth tile's arrow, then click the device name to connect. Or open Settings, Bluetooth and devices, find the device, and select Connect. Windows does not always auto-connect a paired device.
Check the device itself. Make sure it is turned on, charged, and in range. Headphones in their case and speakers in standby will not connect, and a device connected to a phone will usually refuse a second connection.
Toggle Bluetooth off and back on. In Quick Settings, turn Bluetooth off, wait ten seconds, and turn it on again. This clears a hung connection state without touching any pairing.
Restart the Bluetooth Support Service. Press Win + R, type services.msc, and press Enter. Right-click Bluetooth Support Service and select Restart. A stopped service lets devices stay paired while refusing every connection attempt.
Remove the device and pair it again. In Settings, Bluetooth and devices, Devices, select the three dots next to the device, choose Remove device, and confirm. Then put the device in pairing mode and add it fresh, since a corrupted pairing entry is the most common cause of a device that pairs once and never connects again.
Check the audio output if it is a headset or speaker. A connected audio device can still be silent if Windows is sending sound elsewhere. Click the speaker icon on the taskbar, then the arrow next to the volume slider, and select the device as the output.
Update the Bluetooth driver. In Device Manager, expand Bluetooth, right-click the adapter, and select Update driver. If the problem started after an update, try Roll Back Driver on the Driver tab instead.
Removing a device deletes its pairing keys from Windows. You will need to put the device back in pairing mode to add it again, so do not remove it unless you know how to start pairing mode on that device.
If it still happens
If the device connects for a few seconds and then drops, the radio link itself is unstable, so check distance and interference first, then the power management setting that lets Windows turn the adapter off. If it never connects at all on this PC but connects fine to a phone, reinstall the Bluetooth driver from the PC maker's site, since the generic Windows driver sometimes cannot complete the connection handshake.
Common questions
It connects, then disconnects a few seconds later. Why? The link is coming up but not holding, which points to interference, distance, or the adapter being powered down. Move closer, move away from USB 3 devices and microwaves, and turn off the adapter's power saving in Device Manager.
The Connect button does nothing. What now? The stored pairing is probably stale. Remove the device and pair it again from scratch, and restart the Bluetooth Support Service before you try.
Why does Windows connect it but play no sound? Connection and audio output are separate steps. Select the device as the output in the taskbar volume menu, and pick the Stereo entry rather than the Hands-Free entry for music and video.