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Having a Beautiful Tallis: 
It is a Mitzvah to have a beautiful Tallis and beautiful Tzitzis. The same applies for all Mitzvos, as they all must be done with Hiddur [adornment] to the best of one’s ability. [One is thus to launder his Tallis occasionally in order so it be clean and beautiful. Many Poskim have spoken against those that are particular to always wash their clothing, but their Tallis they allow to become dirty and torn. Some Poskim even write that a Tallis which is unwearable due to its dirty and torn state loses its Tzitzis obligation and one may not recite a blessing over it. Although other Poskim negate this opinion, nevertheless it is certainly proper for one to be particular in it and beautify the Mitzvah.]
Is having a beautiful Tallis a Biblical or Rabbinical Mitzvah?
It is disputed amongst Poskim whether the command of Hiddur Mitzvah is Biblical or Rabbinical. Some Poskim rule that having a beautiful Tallis is a Biblical Mitzvah, and so is implied to be the opinion of Admur.
Changing an old Tallis Gadol for a new one:
Some Gedolei Yisrael were accustomed to not change the Tallis they used for prayer, even after the Tallis was torn and worn out, saying that this itself is the Hiddur of the Tallis.
 24/3; M”A 24/1; Shabbos 133b
 The reason: As the verse states “Zeh Keili Veanveihu” which teaches us that one is to beautify himself in Mitzvos before Hashem. [ibid]
 Chesed Lealafim 24/5; Kaf Hachaim 24/3
 Poskim in Kaf Hachaim ibid
 Ashel Avraham Butchach 16 and Siddur Daas Kedoshim; Birchas Habayis 37/8; P”M 16 M”Z 1; Mahariy Ashkenazi 3; Nimukei Orach Chaim 16; See Maharsham 8/10
 M”B in Biur Halacha 16 “Lashuk”; Chesed Leavraham 2; Shinaver in Hakdama to Daas Kedoshim; See also Aruch Hashulchan 16/5; Hisorerus Teshuvah 1/7; Igros Moshe Y.D. 3/52; Tzitz Eliezer 20/8
 Sdei Chemed Klalim Mareches Zayin 12; Maharsham 5/61; Shoel Umeishiv Mahadurah Gimel 3/33; Beis Shlomo 6; Haemek Sheila Shlach 126/5
 Emek Shielia ibid
 Likkutei Sichos 11/241
 So is told of the Taz that when he was approached with a new Tallis he refused to wear it, claiming that his Tallis contains the sweat of all of his prayers and hence he did not want to switch it.