There is a prohibition against destroying fruit trees (Devarim 20:19). Are there any exceptions to this rule? May one cut down a fruit tree that is damaging a nearby house?
Rambam (Melachim 6:8) writes that if the tree is causing any type of damage, one may destroy it.
While the Kaf Hachaim (YD 116:85) writes that one shouldn't destroy a fruit tree to build an extension, most poskim allow one to (See Rosh, Bava Kama 91b; Aruch Hashulchan ibid; Yabia Omer ibid).
R’ Ovadia Yosef (Yabia Omer YD 5:12:5) writes that even when it is permitted to destroy the tree, it is best to sell the tree to a non-Jew first, and let them destroy it. R’ Shmuel Wosner (Shevet Halevi 5:95) writes similarly, though adds that one should also sell him the land on which the tree grows (See Teshuvos Vehanhagos 2:729).
While the Gemara (Pesachim 50b) writes that one who destroys fruit trees will not see a good sign all his life, the poskim (Aruch Hashulchan YD 116:13, Yabia Omer YD 5:12:3, Shevet Halevi 6:112) write that when one does so in a permissible manner, one does not need to be concerned.