At time of posting, OBT and the ranked mode are not live so it is unknown how the mode works (for those future readers).
Make the rewards granted to the player be exclusive from, or greater than, the rewards gained in the normal mode. For example, a greater monetary reward for a ranked match, win specific skins/clothing for reaching certain rankings, and/or titles etc.
Communicate about the ranked mode to the entire player base. Inform them of the additional rewards that can be gained by playing ranked mode via things like tool tips during loading screens or naturally, by having players be inquisitive about exclusive skins/titles/etc. players have from suggestion 1.
Dedicate an area of the home screen to a real-time leaderboard. Have it shown to the whole playerbase automatically when they log in for them to see where they place and who is top etc.
Live events, Twitch events, Youtube events, news updates and discussions. This falls solely on the publishers to push these things and make sure that the ranked scene is reaching beyond just the people who are already playing your game but also those who happen to come across it and are in the gaming area in general. I can't go on Youtube or Twitch without coming across things for CSGO, LoL, Overwatch, Paladins or Smite. I can't go on my Steam activity page without seeing regular updates about leaderboards for Black Squad. Now, obviously I realise most of these games have a very large budget behind them to do these things but the difference between simply putting the game out to market to see what happens and actively investing in promoting the game could be the difference between a short or long lifetime for Ironsight. That doesn't mean I expect annual $1m tournaments but even just simple things like Twitch streams and/or Youtube videos with staff talking about the competitive side of Ironsight to engage the community and reach out to others could be a much needed boost for the playerbase. Run regular tournaments and advertise them across gaming websites. Turn the ranked side of Ironsight into an inviting community rather than just another mode.
The purpose of the 4 suggestions above is to generate buzz around the ranked mode and encourage everyone to play it, not just those who are already competitive natured. This will ensure a healthy ranked mode and not just a casual game with a handful of players in ranked, which in turn will draw in new players.
There are plenty of casual-focused shooters on the market already, and honestly, they offer very little new which has been reflected in their declining population and downfalls.
I have also come across shooters which fail to encourage or promote their ranked modes, opting for a small tab somewhere on the screen instead of pushing it to be the preferred mode. Incorporating a ranked mode as an afterthought in this manner would be a waste of time and effort. I believe MOBAs generally do better at encouraging using this mode through things like avatar frames corresponding to current ranking which is shown across all modes and to all players (There are exceptions of course).
I'll update this post in a moment. I'm writing this on my phone and didn't intend it to be this long, my hand hurts.
Edit - My hand is now better.