Dig and bottle jack, then push it a tad too far the other way (but still within the realm of what works for your gate). Then brace low with 4x4s, remove bottle jack and make sure it has stopped settling before you pour the concrete. Maybe throw some rebar in there, it's cheap.

Mortar and concrete are fine for compression, but the makers may only have put rebar in the far side of that (if any). That means pushing on it might cause it to separate. That's why you should dig and bottle jack.