Hyperlinks within email body work in browser but not Gmail mobile app
To get around the Gmail app not having an option to insert a link into text (hyperlink) on my mobile device I use another mobile app to compose the email first. Currently, the only app I have discovered to be compatible with this trick is Google Docs. I find it works for typing, formatting, inserting images and creating hyperlinks.
To upload from Google Docs into Gmail I am presently only aware of the ability to highlight the planned body of the email in Google Docs then pasting it into Gmail.
Using Google Docs I am aware of the ability to carry over changes to some features of the hypertext. Such as colour, boldness, italics, size, underline. There are possibly more customizable options available before inserting what you have composed into Gmail.
I am unaware of any tricks to create a usable hyperlink of images for use in the Gmail app.
Such a feature outside the “Signature” on Gmail desktop could prove most beneficial.
Orignal Answer
This functionality is not available in gmail app. Here is the link to google forum where you can confirm:
https://productforums.google.com/forum/#!topic/gmail/CdhA_3Z1yTo
You can insert link in the gmail app (like http://www.google.com) in Gmail app which is automatically converted to clickable link when you send the message but if you want hyperlink (like "click here" and when you click on it you are directed to the link to the page) you will have to do it from your browser only. There is no option available in Gmail app to do that.
The alternate solution is to use Microsoft Outlook. Add your google account in Outlook app.
In the compose section long press in the area then you get option to add hyperlink.
Answer after discussion in chat
It seems that the problem is with the gmail app version. If you want to open links received in your gmail app so that you are redirected to the location of message in the same mail you need to have minimum version 8 of gmail app. Verified this as I was able to access the links in my gmail app as well as my browser.
Platforms on which veried the links:
Android 6.0.1 - Gmail Version: 8.1.7.182107449.release
Windows 10 - Chrome: Version 63.0.3239.132
Ubuntu 16.04 (xenial) - Firefox: Version 57.0.4