Practically speaking, there isn't a possibility of accessing 4G connectivity on a 3G phone. You will need to buy a new 4G enabled device for the purpose. Ensure that the phone you buy supports VoLTE.
However, there are some tricks being circulated over the internet about some possibilities about being able to access the same on a 3G smartphone. Though I would not terms them as reliable, you may try the tricks at your own risk.
This method works on Qualcomm chipsets. Please ensure you are running Android Kitkat 4.4.
Steps involved are -
1. Download the Shortcut master app. You can get it from the link https://play.google.com/store/apps/details?id=org.vndnguyen.shortcutmaster.lite&hl=en.
2. After launching the app, tap on Options.
3. Locate Engineering Mode or Service Menu.
4. Under it, choose Change LTE Bands.
5. Change the band to Band 40.
That should do it. However, please note that I have not used this method. It has the risk of making your device unusable. Proceed at your own risk.
Live....and Let Live!