How to remove bolt that is snapped off in brickwork?

Drill a series of very small 1/8" holes around the bolt with masonry bits to make it looser and easier to remove or push into the block wall cavity.... then use a larger anchor/bolt. Or if you still want to try drilling a center hole in the bolt, try using a hardened drill bit like carbide, HSS, cobalt or TTP style...cobalt being the best in most cases. Avoid titanium/ coated bits where the coating can wear off and the bit becomes less useful. Carbide/masonry bits are also very hard and can often be used to drill out bolts or hard metals as well. May need to drill in stages with ever increasing bit sizes to get to a size that an easy out can be used to remove the bolt.

https://arstechnica.com/civis/viewtopic.php?t=4133...

A good video review of best bits to use to drill in hard metals...

https://www.youtube.com/watch?v=pmEeR5MTjrg

You need to use a carbide bit on the bolt and a masonry bit on the brick, the insert an iron or lead plug for the new bolt to fit the gate on.

Look for "easy outs" at your hardware store. They are drill bits with a reverse twist. You need a drill with a reverse feature. The easy outs drill a hole and twist out the broken part at the same time.

You need a cobalt drill bit used at low rpm.

Your metal bits are dull most likely. Hitting it dead center is going to be hard and yes the bolt is hard so you need several small drill bits and if you break one of those off in the hole you are drilling in the bolt...drill bits are even HARDER TO GET OUT. BS&T's and lots of swearing. Smoke them if you got them. Now the fun "REALLY STARTS" Next hardest is the EASYOUT when you break that in the hole too. MORE SWEARING IS NEEDED AND MAYBE PUNCHING THE BRICKWORK WITH YOUR FIST SO THE KNUCKLES BLEED will get rid of the tension as you take a day to heal up and "Think about it" It ain't going on the way you are doing it so maybe readjust the gate higher or lower so you make a new hole. Try, try again.