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You'd need a latch lock, keyed both sides. Something like this.
https://www.amazon.com/Double-Keyed-Gate-Latch-Lock/dp/B07HDF9R4R
However to find one that you could directly swap for that deadbolt could be difficult. You may well need a new lockcase fabricated and welded back into the gate.
To make sure the gate is closed after exit I'd put a overhead door closer on it (the things you have on firedoors) as well.
Go and talk to a local locksmith.
Does a type of lock exist that will always lock when when closed and then require key again to open? Looking to replace this one on the security gate on the front door, as a lot of housemates are too lazy to keep it locked.
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