The pole is a critical patio umbrella part as it holds the entire canopy up. It is most often made of wood, but metal is also fairly common. A pole should be long enough to hold the canopy well above people’s heads when they are standing. And it needs to be strong enough to withstand the substantial wind load placed upon the canopy.
Finding a replacement umbrella pole can be difficult as the pole most often comes with the entire umbrella assembly. For an exact replacement often the only source is the manufacturer, or finding another one of the exact same umbrella type, perhaps at a garage sale.
Repairing important patio umbrella parts such as the pole is possible, but not recommended since the repair can degrade the umbrellas appearance and structural integrity. If the pole has snapped, it may be possible to slide on a larger diameter strong pipe section to cover and support the broken part of the pole. Then affix the repair in place with epoxy and/or screws. The repair would then need to be painted to match the rest of the pole. Unless the fit was perfect or lots of epoxy used, the pole may wobble somewhat.
So instead of repairing, getting a new market umbrella such as those listed on the other pages of this site is a much better option. Many of these include free shipping and in recent years market umbrella prices have become quite reasonable on many of the styles.