If you're referring to a UK TV licence, it doesn't matter what kind of monitor you're using; it's about what you watch (live TV, whether over the air or online, or any use of BBC iPlayer). Watching TV via a computer and a dumb monitor still requires a licence.
(Edited to add: Conversely, merely owning a TV does not require a license; if you're only using it as a computer or gaming monitor, and not watching [online] TV programmes on it, you should be fine.)
https://www.tvlicensing.co.uk/check-if-you-need-one
(Edited to add: Conversely, merely owning a TV does not require a license; if you're only using it as a computer or gaming monitor, and not watching [online] TV programmes on it, you should be fine.)