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.
Jyeshtha Nakshatra - It is a nakshatra of feeling better or higher than others. It represents orderly and justifiable people. It is the most closely connected nakshatra with occult and mystic. For more info on Jyeshtha Nakshatra - https://www.astrosaxena.com/jyeshtnaksh.
Scorpio - As Jyeshtha is a part of Scorpio, Scorpio sign and its representations also become important. Scorpio is the 8th sign of zodiac belt, hence it represents the things and energy related with 8th house of horoscope like Sudden Events, Secrecy, Dark World, Occult Science, Research, Inheritance, Serving Others, Taxes etc. Besides these things sign of Scorpio also represent transformation, means changing the whole nature upside down. This is one sign which is favorite of every Astrologer, because it has maximum secrets, so every astrologer gets maximum scope of researching. This is sign about which no one can tell with precision that what will happen to the planets in it, as it is sign of secrecy itself. Wherever Scorpio falls in your chart, you may have had biggest challenges in making things related with that house more stable. Scorpio is also one of those unique signs which has 2 rulers, i.e. Mars and Ketu. In Western Astrology, Pluto also co-rules Scorpio. All this makes Scorpio a chaotic sign. Scorpio consists of next set of 2 and half nakshatras, i.e. Vishakha, Anuradha and Jyeshtha.
Mercury - As Mercury rules Jyeshtha, Mercury's position and dignity is important to know about the overall functioning of any planet in Jyeshtha.
Mars-Ketu - As Mars-Ketu rules Scorpio, their position and dignity is important to know about the overall functioning of any planet in Jyeshtha/Scorpio.
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 Jyeshtha Nakshatra – Now, Mars's efforts and actions are going in the realm of Jyeshtha, the eldest one. Mars is although in nakshatra of enemy Mercury but it is in own sign. So, dignity-wise Mars is in average position here. This position of Mars can make someone highly ambitious because Jyeshtha is nakshatra of high authority or being in high positions. There is no problem in keeping a high ambition but as Mars is in enemy Mercury's nakshatra, these people can try to achieve those high ambitions through short-cuts or impermissible means. They need to understand that they need to learn the systematic and fair approach of Jyeshtha, the eldest sister, to achieve their ambitions and then only this position can work in their favor. Finding short-cuts may not help here. Another things is that this is nakshatra of people who are high on ego. So, they need to take care that their actions should not be directed towards ego satisfaction and they may not display their ego in front of others due to their achievements.
Also, Jyeshtha is closest nakshatra to occult and research oriented subjects. So,Mars in Jyeshtha can show someone who loves to research, works in research field and possible occult career. Although, Jealousy can be a reason behind their ambitious approach but they should try to gain authority to be fair and justifiable to all just like Jyeshtha in the story.
Role of Mercury – Mercury placement is important to guide Mars in right direction, being Jyeshtha's lord.
Role of Mars-Ketu - As Mars will be in own sign, being Scorpio lord, we need not to see Mars position separately..
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 Jyeshtha. 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 Jyeshtha can work in a chart.