Let’s look at important things here –
Mars - Mars represents our will power, courage, ability to take actions, aggressive nature, anger, our fighting ability, brother, male friends, a boy friend for a girl, a soldier, an athlete and real estate etc.
Ardra - Ardra is nakshatra of transformation, turmoils and chaotic events. This can be most closely related with accidents and emergencies. For more information on Ardra, please check this link - https://www.astrosaxena.com/ardranaksh.
Gemini - As Ardra is part of Gemini, Gemini sign and its representations become important here. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Rahu- As Ardra is ruled by Rahu, Rahu's position and dignity will also have an important role in functioning and results of any planet in Ardra.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Mars in Ardra Nakshatra – This can be real troublesome position due to the malefic nature of Mars & Ardra and then due to Mars weak dignity in Gemini. Ardra is nakshatra of chaotic events and turmoils. As Mars is in weak dignity here, it shows that person's actions or efforts may not have dignified directions. It can mean that person may not have clear sense of right direction in which he should take actions or it can also mean that person can be violent or aggressive by nature. As Mars is in enemy sign, person's actions can be scattered everywhere and may not be streamlined. It can also mean someone who can be aggressive or abusive with his language. At its best level, this position can show a Doctor who is taking care of people going through turmoils in life or a Soldier who is fighting battles on border. So, chaotic events and turmoils will be a major part of this position. Overall, it can be a tricky position which can create a Criminal or one who prevents the crime too. I think the end results would depend largely on position and dignity of Rahu and Mercury as they are ruling Mars.
Role of Mercury – Mercury's position will become important in functioning and results of Mars in Ardra/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Mars will have proper direction about the direction of his path or career.
Role of Rahu - Likewise, Rahu's placement is important to guide Mars in right direction.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Mars in Ardra. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Mars in Ardra can work in a chart.