Few questions, then a couple ideas:
* I wasn't able to find the "TP Link AP 110 router" specifically. Is this the new equipment that you have? https://www.tp-link.com/us/business-networking/omada-sdn-access-point/eap110-outdoor/
* What's your ISP? Cable, DSL, fiber?
* What's your full setup? ISP modem => Old Linksys => EAP110?
* Hypothesis 1: IP assignment between the ISP and the EAP110. You're connecting your modem directly to the EAP. The EAP isn't a router itself, but an Access Point. It does try to get an IP assigned from the modem, but doesn't work well. I would put the old router between the modem and the EAP110 and see what happens.
* Hypothesis 2: Power issues. Looking at the [documentation](https://static.tp-link.com/upload/manual/2022/202203/20220307/1910013169-EAP110_UG.pdf
), when running on PoE, you need to run the EAP110 off of a PoE switch. I'm guessing while the EAP does get some power from what it is currently hooked into, it isn't enough for stable operation. Try connecting the EAP110 to a stable power source and see what happens.