If you are an astrologer and know how to run a chart, you create a birth chart for a person using the longitude and latitude of the new location. You must use the original time zone and time changes in order to get an accurate relocated chart. So if your software changes the time zone when you enter a new location—which they usually do —you need to manually re-enter the original time zone (and also daylight correction, if needed).
Many people do not move that far away from where they were born and that may be the case for you or your clients but even small shifts can change the rising Nakshatra of the ascendant and create a different influence. Sri Jyoti Star and Andrew Foss notes that the Varga charts can shift from one city to the next and this may also create subtle new dimensions for career and relationships even within a regional city or area. Moving shorter distances may change your rising nakshatra and create an impact. I had a client how is Scorpio/Vishakha at birth but when she moved she become Scorpio/Anuradha and noted that she suddenly had more friends and people liked her more which is a quality of that nakshatra.
There are other influences to look for in Astro-locality such as Ayurvedic influences and directional influences of a region. For example the NE is ruled by Jupiter, the Southwest by Rahu. They are enemies. If you have Jupiter in the 1st house or dominant in your chart or if you are Pisces or Sagittarius, you may do better in the NE of our country because those energies are dominating. If you move to the Southwest, ruled by Rahu, you may feel really out of place. Having lived in the Southwest of the United States, a place of connected with outsiders, artists, rebels and outlaws you may have a problem if you need Jupiter’s sense of community and expansion and this was the case with my wife.
Ayurvedic tendencies would have to be taken into account. If the person is a fire sign or has a fire imbalance (pitta) in the natal chart, you would not send them to the South where the heat might be too dominant for their health and naturally they will not want to go there anywhere.
There are other factors in astro-locality like latitudinal lines which the software program Solar Fire can generate. For example, I have a Jupiter line going across I-80 in the United States and I have always loved San Francisco and do well near I-80. (Lines on a map by the way have a 50 mile impact in a positive or negative way and that technique will be covered in my course.) I also thinking that living close to your Atmakaraka direction can be beneficial as I was always attracted to the West and Saturn is my Atmakaraka and I flourish in the West.
So you can see there are many factors impacting Astro-locality and because Vedic astrology is more microscopic, it can reveal more subtle dimensions even if you do not move to a foreign country or far away from where you are born. I think that a lot of astrological readings miss the mark because they fail to take into account the new location where someone is living and read the chart from there and my readings always do so if a person has moved far enough away from their birth place. Special thanks to my Jyotish Gurus and especially to Hank Friedman and Andrew Foss for their research and contributions on this subject.