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Make sure the old detector isn't just signifying an objection to some impurities, a few specks of really fine dust, in the air around it.
Leave the battery out for a day or two (and unplugged.)
Make sure the battery you give it is genuinely OK - not cheap, not sat-on-shelf-for-many-months, etc. Or measure it under load to make sure it's OK.
Blow out the detector module inside it, with canned air that is free of microscopic impurities.
Then in an hour or so, put the new battery in again. Let it sit for a quarter hour or so before putting it back in the ceiling mount after plugging it in, to see if it chirps again.
If it persists... it's a good question what to replace it with. The battery may be backup, though, and the wires in the ceiling supposed to actually provide power. If either those wires are not providing power, or the wires to the battery are broken off, then it will chirp in protest.
And if there is dust accumulated on the cover over the detector, particles from that could be getting in the detector.
So clean the outer cover with a vacuum cleaner hose, and also check the wires from the ceiling for adequate voltage supplied. Those measures may cure the problem.
Replacement? either forget the wires in the ceiling, or else look for a replacement that
A. works, provably, not just Used junk
B. has an outlet or jack to match those wires in the ceiling.
I suspect that your type of smoke detector is so old that it has no replacement - they all run off nothing but the battery nowadays, I strongly suspect.
Is having a power/signal plug vital to you in any way, for your s. d. ?
I think you can mount the new one right over the old electrical mounting. From what I've seen and what I know, the detector has the 'pins' on it, so you should be able to fit a non-wired detector on the same spot instead of leaving the peculiar-looking plug in the open - unsightly and, unless it is internally disconnected, quite possibly not safe. Or even, not 'to code'. (I'm admittedly not informed about any such code re such an 'outlet' for smoke detectors.)
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