At our Shul, we do not say Tachanun at Mincha. This apparently is the Shul’s custom for the past 35-40 years, (3 Rabbis ago). A group of us here at the Shul don’t understand why we do not say Tachanun at Mincha, as it is certainly in "Seder Haqtefila". We are now in the process of looking for a new Rabbi and the question of instituting Tachanun at Mincha came up. There are those who feel that this is the time to make the change, as a new Rabbi will come into something that has been made part of our davening. On the other hand, there is an opinion that one does not change an old "Minhag Hamakom" even in Tefilla. Please let me know your thoughts on the matter. Thank you

ב"ה Shalom Your question is certainly in place. There is no doubt that Tachanun at mincha has unjustifiably suffered over the years. Sometimes people daven mincha at the workplace where there is no Aron kodesh or people start mincha late and mincha continues until after Shki'ah so Tachanun is not said. Not to mention that Tachanun is skipped at Mincha erev Shabbat and Chag. On the other hand there is an established minhag not to say Tachanun at mincha at all. (פתחי תשובות סי' קלא:יג) The main reason being that in Chutz La'aretz where shkiah is longer, some communities would finish mincha after the shkiah according to the Geonim so it was decided not to say Tachanun at all even when they Daven before shkiah. However, there is no justification for this minhag in Eretz Yisrael where the shkiah is shorter. Even so there are still those who based upon the Ari z"l do not say Tachanun at Mincha, and the poskim say that someone who participates at such a minyan should not be different and neither should he say Tachanun. Now assuming the first Rabbi of your Shul was part of the decision not to say Tachanun, there is a basis not to say it. Still on the other hand, even if you chose a new Rabbi, changing the Minhag of the Shul needs the agreement of the Kehilla to do so and of course the new Rabbi will has his own say in the matter. )See שו"ת שבט הלוי חלק י סימן יג ד"ה תשובה: כל,( שו"ת אגרות משה אורח חיים חלק ב סימן כא The main thing is that everything should be done in a peaceful manner All the best