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A WiFi access point to turn the data in the ethernet cable into wireless internet.
A router won't work, you need to plug the ethernet cable into your router at the house end and have an access point at the other.
Last time I checked the forum recommended one was the UAP-AC-LITE (https://eu.store.ui.com/products/unifi-ac-lite) or the Access Point WiFi 6 Lite (https://eu.store.ui.com/collections/unifi-network-wireless/products/unifi-ap-6-lite) if you want the latest standard/a bit faster.
Other WiFi access points are no doubt available but won't be as good ;)
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It might be worth having a switch at the end in the office too, so that you can have ethernet to devices if you need (and have a wireless access point as well).
Here's a switch / AP combo on ebay. POE switches are useful for cameras and the like.
I have 2 ethernet cables heading to my garden room, connected to an 8 port switch (one is for redundancy, in case fences blow over).
That is connected to a wireless AP, ethernet ports in the office part of the building, a couple of other nerdy things, and a couple spare.
Just built a garden office which is about 25 metres from the router in the house. We have an ethernet cable running from the house down to the office, what do I need to transmit the internet from that wire to the office wirelessly?
Sorry if badly worded question, there's so many different products out there and its confusing to know what's what.
Edit: Would something like this work? https://www.amazon.co.uk/TP-Link-TL-WR841N-300Mbps-Wireless-Supports/dp/B001FWYGJS/ref=sr_1_4?crid=2TSZ2TUN8FRY6