Remove and Change some texts of a URL in an HTML using Javascript

I'd suggest, in plain-JavaScript (as your question doesn't imply your use of any libraries, such as jquery for example):

// wrapped the function as an 'Immediately-Invoked Function Expression' (IIFE)
// so that it'll be called automatically, when encountered:
(function () {
// gets all the images on the page:
    var images = document.querySelectorAll('img'),
// creates an '<a>' element:
        link = document.createElement('a'),
// creates a variable (for later use, within the 'forEach()'):
        newLink;

// uses 'Array.prototype.forEach()' to iterate over the images:
    [].forEach.call(images, function (img) {

    // checks that 'instagram.com' is in the 'src' of the current image:
        if (img.src.indexOf('instagram.com') > -1) {
            // if it is, we clone the created-'a' element:
            newLink = link.cloneNode();

            // set the 'href' of the '<a>' to the 'src' of the image,
            // but first we replace '_s' with '_n', and
            // any sequence of characters starting with a '/' followed by
            // 't51' continuing with alphanumeric characters (a-z, 0-9,
            // case-insensitive) periods ('.') or hyphens ('-') with an
            // empty string (removing that sequence from the 'src'):
            newLink.href = img.src.replace(/(_s)|(\/t51[\w\d.-]+)/g,function (match){
                return match === '_s' ? '_n' : '';
            });

            // insert the '<a>' element before the image:
            img.parentNode.insertBefore(newLink,img);
            // move the image into the '<a>':
            newLink.appendChild(img);
        }
    });
})();

JS Fiddle demo.

This should be placed immediately before the closing </body> tag; in order to run after the DOM has been constructed.

References:

• Array.prototype.forEach().
• document.querySelectorAll().
• JavaScript Regular Expressions.
• Node.appendChild().
• Node.cloneNode().
• Node.insertBefore().
• String.prototype.replace().