I own a chiming mantle clock – I think it is a Smith Enfield movement, made about 1955.
Brass movement inside a wooden case. Presented to my father on his retirement. Label inside says "Repairs – E. Hitchcock and Son, Watchmakers, Market Place, Bingham."

8 day movement, two keys (one for chimes, hour and half hour, one for time).

It used to keep perfect time. Recently it started losing large amounts of time, even though the movement was still working.

The displayed time is adjusted by moving the minute hand. What seems to be happening is that the drive to the minute hand is through a slipping clutch – the minute hand is fitted to a long hollow cylinder, and the drive from the movement appears to be a shaft which is a sliding fit into the cylinder.
I would guess that the drive shaft should be a tight friction fit inside the minute hand cylinder. But now it is too loose, and the weight of the minute hand when pointing to 9 o'clock is enough to cause it to clip when it gets to this point.

Can anyone suggest a cure?

By a knurled nut. The hand has a square hole, which ehgages with a square on the drive shaft.

I can see the star-shaped tension spring, and what looks like a hole in the arbor which may once have held a pin – but there's no sign of the pin. Does it need a special pin, or would some wire passed through the hole do the same job?
Is it possible to compress the star-shaped spring and fit a pin, without taking the back-plate off the clock?

If I do take the back plate off (I'm a bit nervous about this!), do I need to ensure that both the power springs are wound down fully? Then there are 10 shafts which will need re-engaging to put the back plate back in position.

This is new territory for me – all I've done previously is to remove the movement from the case, and then clean and oil the bearings. I've (in my youth) dismantled and re-assembled small bedside alarm clocks – this is much more complex.

Thanks for the advice, Stephen.
I'll have a go with my long-nosed pliars (probably tomorrow), and let you know how I'm getting on.