The clutch does not regulate speed. That is the job of the motor at the capstan. The takeup wheel is always overdriven speed-wise and so the clutch is always slipping to maintain tension.
It is typically a cloth disk compressed between two plastic disks, like a miniature car clutch. It depends on the quality of the tape mechanism, cheap or high-end, auto-reverse etc.
Back in the day used a takeup torque gauge but eventually you can put your finger on the hub during playback and judge if there is enough takeup torque. Required highest on cheap and long i.e. C-120 cassettes.
If the deck falsely auto-stops, you can see the takeup hub stop turning now and then. It can also be caused by belt slippage, or an idler wheel slipping- whatever drives the takeup wheel. Or the hub sensors (magnet+reed switch) not working or cutting out. It will "eat tapes" if the takeup hub is too slow, makes a mess.
To fix them, remove the plastic C-clip and take out the hub with clutch assembly. Don't lose any washers.
We would dunk and soak them a while in IPA, turn the clutch, and pull the wheels apart and sometimes clean in there. But rarely, a clutch will wear out, or get oil/grease contamination on the cloth disk. Then dry out the clutch and the torque is usually much better.
You have to be careful here, any oil/grease will easily get in the clutch or the belt or idler pulley. It only goes on the metal pin if you lube it during reassembly.