I had the mower sitting for a year. I cleaned the carburator and put a new battery. Runs very well now. However, when I put it in gear reverse or forward it does not engage. It is not the brake, do these transmission use oil. I have never checked.

Did you change the engine oil and filter?
Find the manual for your make, model, and year online.

Check for a transmission linkage. On mine it's a thin rod bent an inch at the end, at the back of the mower, that goes under the seat all the way to the transmission. Goes out about 3" to disengage. Yours might be disengaged. A must if you tow it backwards.

Turn it and put it back in. That should do it.