No idea what that white stuff is. Looks like chewing gum?

It looks like this has been happening for a while because of the score marks on the motor shaft, so one has to wonder how worn the pulley bore is.

I’d suggest getting both scrupulously clean first, then seeing exactly how loose the pulley is on the shaft. If it’s a sliding fit but not sloppy and wobbly, then put a couple of drops of Loktite 648 in the pulley bore, fit it and leave for 24 hours. Make sure it stays out of the motor bearings! (You could use superglue but you run the risk of it setting before you’ve got the pulley in the correct position.)

If the pulley is so worn that it wobbles let me know and I’ll dig out my spare one.