Is it possible to enable http compression for requests?

To PUT data to the server compressed you must compress the request body and set the Content-Encoding: gzip header. The header itself must be uncompressed. It's documented in mod_deflate:

The mod_deflate module also provides a filter for decompressing a gzip compressed request body. In order to activate this feature you have to insert the DEFLATE filter into the input filter chain using SetInputFilter or AddInputFilter.

...

Now if a request contains a Content-Encoding: gzip header, the body will be automatically decompressed. Few browsers have the ability to gzip request bodies. However, some special applications actually do support request compression, for instance some WebDAV clients.

And an article describing it is here:

So how do you do it? Here is a blurb, again from the mod_deflate source code: only work on main request/no subrequests. This means that the whole body of the request must be gzip compressed if we chose to use this, it is not possible to compress only the part containing the file for example in a multipart request.

Separately, a browser can request server response content to be compressed by setting Accept-Encoding header as per here:

GET /index.html HTTP/1.1
Host: www.http-compression.com
Accept-Encoding: gzip
User-Agent: Firefox/1.0

This will return compressed data to the browser.

Answering the part about compressed requests, not responses: yes, it is possible, even if it does not seem in widespread usage. The client-side app needs to set the appropriate content-encoding header. As for the server-side app, there are 2 choices:

1. the app supports reinflating the request body by itself. An example library which can do this is the phpxmlrpc one.

2. the webserver inflates the response body before passing it to the app. This is possible using f.e. the mod_deflate filter of Apache and setting up an inputFilter

Not natively from any browser I know of, you'd have to find a plugin that would do it for you. You basically have to set the content-encoding HTTP header to let the server know how the request is coming in. The server, of course, needs to be able to handle that encoding.

Below code is setup the custom header and pass this header in api call as http options :

getCustomHeaders() {
    return new HttpHeaders({
      'Accept-Encoding': 'gzip, deflate'
    });
}

After that while you calling the API to get the data , pass the options with url:

searchData(title: string, type: SearchType): Observable<any> {
    const headersSpl = this.getCustomHeaders();
    const httpOptions = {
      headers : headersSpl
    };
    const url = `${this.url}?s=${encodeURI(title)}&type=${type}&apiKey=${this.apiKey}`;
    return this.httpClient.get(url, httpOptions)
    .pipe(
      map( results => results['data']),
      catchError( error => { console.log(error); return EMPTY })
    )
  }

This is NOT allowed. According to the HTTP specification (RFC 2616), Content-Encoding is NOT one of the possible request header fields, therefore it is not possible to compress the request entity body as there is no legal way to let the server know this has occurred. Any compression of the request body is done only as a non-standard extension.