Related Achievements: Corporal Punishment, Sergeant at Arms
In Tour of Duty (which you can access by hitting left trigger on the home screen) you need to reach the rank of Captain by obtaining stars. You can obtain stars by completing daily challenges and by earning medals.
Daily challenges are, well daily, and can be accessed from the Tour of Duty menu. In Gears 5 there are four daily challenges per day - two 'general' challenges, one 'versus' challenge, and one 'horde/escape' challenge. These challenges can range anywhere from completing one horde match to getting twenty kills with shotguns. Every day you can 'refresh' one challenge for a new one of the same category. Try to complete all four each day to 'rank-up' as quickly as possible.
Daily Challenges Helpful Link: https://twinfinite.net/2019/09/gears-5-tour-of-duty-objectiv...
Medals more long-term ways to earn stars. There are different 'sets' of medals including:
Some examples include 1000 head shot kills, 30 boss eliminations in horde/escape, and building 300 fortifications as Del. As long as you are aware of which medals are attainable for you and actively work toward obtaining these medals it should be fairly easy to grab these extra stars and rank up.
Medals Helpful Link: https://gearsofwar.fandom.com/wiki/Tour_of_Duty
Reward: Team Rock Weapon Skins (Legendary) upon completion.